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Renormalizability of pure $\mathcal{N}=1$ Super Yang-Mills in the
Wess-Zumino gauge in the presence of the local composite operators $A^{2}$
and $\barλλ$: The renormalization of $\mathcal{N}=1$ Super Yang-Mills theory with the
presence of the local composite operators $AA$, $A_\mu \gamma_\mu \lambda$ and
$\bar{\lambda}\lambda$ is analyzed in the Wess-Zumino gauge, employing the
Landau condition. An all-orders proof of the renormalizability of the theory is
given by means of the Algebraic Renormalization procedure. Only three
renormalization constants are needed, which can be identified with the coupling
constant, gauge field, and gluino renormalization. The non-renormalization
theorem of the gluon--ghost--anti-ghost vertex in the Landau gauge is shown to
remain valid in $\mathcal{N}=1$ Super Yang-Mills with the presence of the local
composite operators. Moreover, due to the non-linear realization of the
supersymmetry in the Wess-Zumino gauge, the renormalization factor of the gauge
field turns out to be different from that of the gluino. | A geometrical approach to super W-induced gravities in two dimensions: A geometrical study of supergravity defined on (1|1) complex superspace is
presented. This approach is based on the introduction of generalized
superprojective structures extending the notions of super Riemann geometry to a
kind of super W-Riemann surfaces. On these surfaces a connection is
constructed. The zero curvature condition leads to the super Ward identities of
the underlying supergravity. This is accomplished through the symplectic form
linked to the (super)symplectic manifold of all super gauge connections. The
BRST algebra is also derived from the knowledge of the super W-symmetries which
are the gauge transformations of the vector bundle canonically associated to
the generalized superprojective structures. We obtain the possible consistent
BRST (super)anomalies and their cocycles related by the descent equations.
Finally we apply our considerations to the case of supergravity. |
Lectures on Twistor Strings and Perturbative Yang-Mills Theory: Recently, Witten proposed a topological string theory in twistor space that
is dual to a weakly coupled gauge theory. In this lectures we will discuss
aspects of the twistor string theory. Along the way we will learn new things
about Yang-Mills scattering amplitudes. The string theory sheds light on
Yang-Mills perturbation theory and leads to new methods for computing
Yang-Mills scattering amplitudes. | Competing s-wave orders from Einstein-Gauss-Bonnet gravity: In this paper, the holographic superconductor model with two s-wave orders
from 4+1 dimensional Einstein-Gauss-Bonnet gravity is explored in the probe
limit. At different values of the Gauss-Bonnet coefficient $\alpha$, we study
the influence of tuning the mass and charge parameters of the bulk scalar field
on the free energy curve of condensed solution with signal s-wave order, and
compare the difference of tuning the two different parameters while the changes
of the critical temperature are the same. Based on the above results, it is
indicated that the two free energy curves of different s-wave orders can have
one or two intersection points, where two typical phase transition behaviors of
the s+s coexistent phase, including the reentrant phase transition near the
Chern-Simons limit $\alpha=0.25$, can be found. We also give an explanation to
the nontrivial behavior of the $T_c-\alpha$ curves near the Chern-Simons limit,
which might be heuristic to understand the origin of the reentrant behavior
near the Chern-Simons limit. |
Virasoro Representations on Fusion Graphs: For any non-unitary model with central charge c(2,q) the path spaces
associated to a certain fusion graph are isomorphic to the irreducible Virasoro
highest weight modules. | Coordinate representation of particle dynamics in AdS and in generic
static spacetimes: We discuss the quantum dynamics of a particle in static curved spacetimes in
a coordinate representation. The scheme is based on the analysis of the squared
energy operator E^2, which is quadratic in momenta and contains a scalar
curvature term. Our main emphasis is on AdS spaces, where this term is fixed by
the isometry group. As a byproduct the isometry generators are constructed and
the energy spectrum is reproduced. In the massless case the conformal symmetry
is realized as well. We show the equivalence between this quantization and the
covariant quantization, based on the Klein-Gordon type equation in AdS. We
further demonstrate that the two quantization methods in an arbitrary
(N+1)-dimensional static spacetime are equivalent to each other if the scalar
curvature terms both in the operator E^2 and in the Klein-Gordon type equation
have the same coefficient equal to (N-1)/(4N). |
U(1) lattice gauge theory and N=2 supersymmetric Yang-Mills theory: We discuss the physics of four-dimensional compact U(1) lattice gauge theory
from the point of view of softly broken N=2 supersymmetric SU(2) Yang-Mills
theory. We provide arguments in favor of (pseudo-)critical mass exponents 1/3,
5/11 and 1/2, in agreement with the values observed in the computer
simulations. We also show that the J^{CP} assignment of some of the lowest
lying states can be naturally explained. | QED_2+1: the Compton effect: The Compton effect in a two-dimensional world is compared with the same
process in ordinary three-dimensional space. |
Josephson Junctions and AdS/CFT Networks: We propose a new holographic model of Josephson junctions (and networks
thereof) based on designer multi-gravity, namely multi-(super)gravity theories
on products of distinct asymptotically AdS spacetimes coupled by mixed boundary
conditions. We present a simple model of a Josephson junction (JJ) that
exhibits the well-known current-phase sine relation of JJs. In one-dimensional
chains of holographic superconductors we find that the Cooper-pair condensates
are described by a discretized Schrodinger-type equation. Such non-integrable
equations, which have been studied extensively in the past in condensed matter
and optics applications, are known to exhibit complex behavior that includes
periodic and quasiperiodic solutions, chaotic dynamics, soliton and kink
solutions. In our setup these solutions translate to holographic configurations
of strongly-coupled superconductors in networks with weak site-to-site
interactions that exhibit interesting patterns of modulated superconductivity.
In a continuum limit our equations reduce to generalizations of the
Gross-Pitaevskii equation. We comment on the many possible extensions and
applications of this new approach. | Holographic Aspects of Four Dimensional ${\cal N }=2$ SCFTs and their
Marginal Deformations: We study the holographic description of ${\cal N}=2$ Super Conformal Field
Theories in four dimensions first given by Gaiotto and Maldacena. We present
new expressions that holographically calculate characteristic numbers of the
CFT and associated Hanany-Witten set-ups, or more dynamical observables, like
the central charge. A number of examples of varying complexity are studied and
some proofs for these new expressions are presented. We repeat this treatment
for the case of the marginally deformed Gaiotto-Maldacena theories, presenting
an infinite family of new solutions and compute some of its observables. These
new backgrounds rely on the solution of a Laplace equation and a boundary
condition, encoding the kinematics of the original conformal field theory. |
Extremal Black Holes in Supergravity and the Bekenstein-Hawking Entropy: We review some results on the connection among supergravity central charges,
BPS states and Bekenstein-Hawking entropy. In particular, N=2 supergravity in
four dimensions is studied in detail. For higher N supergravities we just give
an account of the general theory specializing the discussion to the N=8 case
when one half of supersymmetry is preserved. We stress the fact that for
extremal supergravity black holes the entropy formula is topological, that is
the entropy turns out to be a moduli independent quantity and can be written in
terms of invariants of the duality group of the supergravity theory. | Perturbations of Self-Accelerated Universe: We discuss small perturbations on the self-accelerated solution of the DGP
model, and argue that claims of instability of the solution that are based on
linearized calculations are unwarranted because of the following: (1) Small
perturbations of an empty self-accelerated background can be quantized
consistently without yielding ghosts. (2) Conformal sources, such as radiation,
do not give rise to instabilities either. (3) A typical non-conformal source
could introduce ghosts in the linearized approximation and become unstable,
however, it also invalidates the approximation itself. Such a source creates a
halo of variable curvature that locally dominates over the self-accelerated
background and extends over a domain in which the linearization breaks down.
Perturbations that are valid outside the halo may not continue inside, as it is
suggested by some non-perturbative solutions. (4) In the Euclidean continuation
of the theory, with arbitrary sources, we derive certain constraints imposed by
the second order equations on first order perturbations, thus restricting the
linearized solutions that could be continued into the full nonlinear theory.
Naive linearized solutions fail to satisfy the above constraints. (5) Finally,
we clarify in detail subtleties associated with the boundary conditions and
analytic properties of the Green's functions. |
Five-loop Konishi in N=4 SYM: We present a new method for computing the Konishi anomalous dimension in N=4
SYM at weak coupling. It does not rely on the conventional Feynman diagram
technique and is not restricted to the planar limit. It is based on the OPE
analysis of the four-point correlation function of stress-tensor multiplets,
which has been recently constructed up to six loops. The Konishi operator gives
the leading contribution to the singlet SU(4) channel of this OPE. Its
anomalous dimension is the coefficient of the leading single logarithmic
singularity of the logarithm of the correlation function in the double
short-distance limit, in which the operator positions coincide pairwise. We
regularize the logarithm of the correlation function in this singular limit by
a version of dimensional regularization. At any loop level, the resulting
singularity is a simple pole whose residue is determined by a finite two-point
integral with one loop less. This drastically simplifies the five-loop
calculation of the Konishi anomalous dimension by reducing it to a set of known
four-loop two-point integrals and two unknown integrals which we evaluate
analytically. We obtain an analytic result at five loops in the planar limit
and observe perfect agreement with the prediction based on integrability in
AdS/CFT. | Quantum phase transitions in semi-local quantum liquids: We consider several types of quantum critical phenomena from finite-density
gauge-gravity duality which to different degrees lie outside the
Landau-Ginsburg-Wilson paradigm. These include: (1) a "bifurcating" critical
point, for which the order parameter remains gapped at the critical point, and
thus is not driven by soft order parameter fluctuations. Rather it appears to
be driven by "confinement" which arises when two fixed points annihilate and
lose conformality. On the condensed side, there is an infinite tower of
condensed states and the nonlinear response of the tower exhibits an infinite
spiral structure; (2) a "hybridized" critical point which can be described by a
standard Landau-Ginsburg sector of order parameter fluctuations hybridized with
a strongly coupled sector; (3) a "marginal" critical point which is obtained by
tuning the above two critical points to occur together and whose bosonic
fluctuation spectrum coincides with that postulated to underly the "Marginal
Fermi Liquid" description of the optimally doped cuprates. |
Flow equations for generalised $T\bar{T}$ deformations: We consider the most general set of integrable deformations extending the
$T\bar{T}$ deformation of two-dimensional relativistic QFTs. They are CDD
deformations of the theory's factorised S-matrix related to the higher-spin
conserved charges. Using a mirror version of the generalised Gibbs ensemble, we
write down the finite-volume expectation value of the higher-spin charges, and
derive a generalised flow equation that every charge must obey under a
generalised $T\bar{T}$ deformation. This also reproduces the known flow
equations on the nose. | Wilson Loops in the Large N Limit at Finite Temperature: Using a proposal of Maldacena we compute in the framework of the supergravity
description of N coincident D3 branes the energy of a quark anti-quark pair in
the large N limit of U(N) N=4 SYM in four dimensions at finite temperature. |
Analysis of Maxwell Equations in a Gravitational Field: In a gravitational field, we analyze the Maxwell equations, the correponding
electromagnetic wave and continuity equations. A particular solution for
parellel electric and magnetic fields in a gravitational background is
presented. These solutions also satisfy the free-wave equations and the
phenomenology suggested by plasma physics. | The (p,q) String Tension in a Warped Deformed Conifold: We find the tension spectrum of the bound states of p fundamental strings and
q D-strings at the bottom of a warped deformed conifold. We show that it can be
obtained from a D3-brane wrapping a 2-cycle that is stabilized by both electric
and magnetic fluxes. Because the F-strings are Z_M-charged with non-zero
binding energy, binding can take place even if (p,q) are not coprime.
Implications for cosmic strings are briefly discussed. |
A $U(3)$ Gauge Theory on Fuzzy Extra Dimensions: In this article, we explore the low energy structure of a $U(3)$ gauge theory
over spaces with fuzzy sphere(s) as extra dimensions. In particular, we
determine the equivariant parametrization of the gauge fields, which transform
either invariantly or as vectors under the combined action of $SU(2)$ rotations
of the fuzzy spheres and those $U(3)$ gauge transformations generated by $SU(2)
\subset U(3)$ carrying the spin $1$ irreducible representation of $SU(2)$. The
cases of a single fuzzy sphere $S_F^2$ and a particular direct sum of
concentric fuzzy spheres, $S_F^{2 \, Int}$, covering the monopole bundle
sectors with windings $\pm 1$ are treated in full and the low energy degrees of
freedom for the gauge fields are obtained. Employing the parametrizations of
the fields in the former case, we determine a low energy action by tracing over
the fuzzy sphere and show that the emerging model is abelian Higgs type with
$U(1) \times U(1)$ gauge symmetry and possess vortex solutions on ${\mathbb
R}^2$, which we discuss in some detail. Generalization of our formulation to
the equivariant parametrization of gauge fields in $U(n)$ theories is also
briefly addressed. | Quaternionic structures, supertwistors and fundamental superspaces: Superspace is considered as space of parameters of the supercoherent states
defining the basis for oscillator-like unitary irreducible representations of
the generalized superconformal group SU(2m,2n/2N) in the field of quaternions
H. The specific construction contains naturally the supertwistor one of the
previous work by Litov and Pervushin [1] and it is shown that in the case of
extended supersymmetry such an approach leads to the separation of a class of
superspaces and and its groups of motion. We briefly discuss this particular
extension to the domain of quaternionic superspaces as nonlinear realization of
some kind of the affine and the superconformal groups with the final end to
include also the gravitational field[6] (this last possibility to include
gravitation, can be realized on the basis of the reference[12] where the coset
((Sp(8))/(SL(4R)))~((SU(2,2))/(SL(2C)))was used in the non supersymmetric
case). It is shown that this quaternionic construction avoid some
unconsistencies appearing at the level of the generators of the superalgebras
(for specific values of p and q; p+q=N) in the twistor one. |
On certain cosmological relics of the early string dynamics: The tracing of cosmological relics from the early string dynamics may enhance
the theory and provide new perspectives on the major cosmological problems.
This point is illustrated in a leading-order Bianchi-type $VII_0$ string
background, wherein spatial isotropy can be claimed as such a relic. A much
finer one, descending from a premordial gravitational wave, could be retrieved
from its imprint on the small-scale structure of the cosmic microwave
background. In spite of the absence of conventional inflation, there is no
horizon problem thanks to the presence of an equally fundamental mixmaster
dynamics. Implications and certain new perspectives which thus arise for the
more general problem of cosmological mixing are briefly discussed. | Effect of rotation symmetry to abelian Chern-Simons field theory and
anyon equation on a sphere: We analyze the Chern-Simons field theory coupled to non-relativistic matter
field on a sphere using canonical transformation on the fields with special
attention to the role of the rotation symmetry: SO(3) invariance restricts the
Hilbert space to the one with a definite number of charges and dictates Dirac
quantization condition to the Chern-Simons coefficient, whereas SO(2)
invariance does not. The corresponding Schr\"odinger equation for many anyons
(and for multispecies) on the sphere are presented with appropriate boundary
condition. In the presence of an external magnetic monopole source, the ground
state solutions of anyons are compared with monopole harmonics. The role of the
translation and modular symmetry on a torus is also expounded. |
Quantum fluctuations in the DGP model and the size of the cross-over
scale: The Dvali-Gabadadze-Porrati model introduces a parameter, the cross-over
scale $r_c$, setting the scale where higher dimensional effects are important.
In order to agree with observations and to explain the current acceleration of
the Universe, $r_c$ must be of the order of the present Hubble radius. We
discuss a mechanism to generate a large $r_c$, assuming that it is determined
by a dynamical field and exploiting the quantum effects of the graviton. For
simplicity, we consider a scalar field $\Psi$ with a kinetic term on the brane
instead of the full metric perturbations. We compute the Green function and the
1-loop expectation value of the stress tensor of $\Psi$ on the background
defined by a flat bulk and an inflating brane (self-accelerated or not). We
also include the flat brane limit. The quantum fluctuations of the bulk field
$\Psi$ provide an effective potential for $r_c$. For a flat brane, the 1-loop
effective potential is of the Coleman-Weinberg form, and admits a minimum for
large $r_c$ without fine tuning. When we take into account the brane curvature,
a sizeable contribution at the classical level changes this picture and the
potential develops a (minimum) maximum for the (non-) self-accelerated branch. | Massless Monopoles and Multipronged Strings: We investigate the role of massless magnetic monopoles in the N=4
supersymmetric Yang-Mills Higgs theories. They can appear naturally in the
1/4-BPS dyonic configurations associated with multi-pronged string
configurations. Massless magnetic monopoles can carry nonabelian electric
charge when their associated gauge symmetry is unbroken. Surprisingly, massless
monopoles can also appear even when the gauge symmetry is broken to abelian
subgroups. |
Generalised Complex Geometry and the Planck Cone: Complex geometry and symplectic geometry are mirrors in string theory. The
recently developed generalised complex geometry interpolates between the two of
them. On the other hand, the classical and quantum mechanics of a finite number
of degrees of freedom are respectively described by a symplectic structure and
a complex structure on classical phase space. In this letter we analyse the
role played by generalised complex geometry in the classical and quantum
mechanics of a finite number of degrees of freedom. We identify generalised
complex geometry as an appropriate geometrical setup for dualities. The latter
are interpreted as transformations connecting points in the interior of the
Planck cone with points in the exterior, and viceversa. The Planck cone bears
some resemblance with the relativistic light-cone. However the latter cannot be
traversed by physical particles, while dualities do connect the region outside
the Planck cone with the region inside, and viceversa. | On the Relationship between the Uniqueness of the Moonshine Module and
Monstrous Moonshine: We consider the relationship between the conjectured uniqueness of the
Moonshine Module, ${\cal V}^\natural$, and Monstrous Moonshine, the genus zero
property of the modular invariance group for each Monster group Thompson
series. We first discuss a family of possible $Z_n$ meromorphic orbifold
constructions of ${\cal V}^\natural$ based on automorphisms of the Leech
lattice compactified bosonic string. We reproduce the Thompson series for all
51 non-Fricke classes of the Monster group $M$ together with a new relationship
between the centralisers of these classes and 51 corresponding Conway group
centralisers (generalising a well-known relationship for 5 such classes).
Assuming that ${\cal V}^\natural$ is unique, we then consider meromorphic
orbifoldings of ${\cal V}^\natural$ and show that Monstrous Moonshine holds if
and only if the only meromorphic orbifoldings of ${\cal V}^\natural$ give
${\cal V}^\natural$ itself or the Leech theory. This constraint on the
meromorphic orbifoldings of ${\cal V}^\natural$ therefore relates Monstrous
Moonshine to the uniqueness of ${\cal V}^\natural$ in a new way. |
Exploring Reggeon bound states in strongly-coupled $\mathcal{N}=4$ super
Yang-Mills: The multi-Regge limit of scattering amplitudes in strongly-coupled
$\mathcal{N}=4$ super Yang-Mills is described by the large mass limit of a set
of thermodynamic Bethe ansatz (TBA) equations. A non-trivial remainder function
arises in this setup in certain kinematical regions due to excitations of the
TBA equations which appear during the analytic continuation into these
kinematical regions. So far, these analytic continuations were carried out on a
case-by-case basis for the six- and seven-gluon remainder function. In this
note, we show that the set of possible excitations appearing in any analytic
continuation in the multi-Regge limit for any number of particles is rather
constrained. In particular, we show that the BFKL eigenvalue of any possible
Reggeon bound state is a multiple of the two-Reggeon BFKL eigenvalue appearing
in the six-gluon case. | AdS_3/CFT_2 Correspondence and Space-Time N=3 Superconformal Algebra: We study a Wess-Zumino-Witten model with target space AdS_3 x (S^3 x S^3 x
S^1)/Z_2. This allows us to construct space-time N=3 superconformal theories.
By combining left-, and right-moving parts through a GSO and a Z_2 projections,
a new asymmetric (N,\bar{N})=(3,1) model is obtained. It has an extra gauge
(affine) SU(2) symmetry in the target space of the type IIA string. An
associated configuration is realized as slantwise intersecting M5-M2 branes
with a Z_2-fixed plane in the M-theory viewpoint. |
Spectral-integral representation of the photon polarization operator in
a constant uniform magnetic field: The polarization operator in a constant and homogeneous magnetic field of
arbitrary strength is investigated on mass shell. The calculations are carried
out at all photon energies higher the pair creation threshold as well as lower
this threshold. The general formula for the effective mass of the photon with
given polarization has been obtained being useful for an analysis of the
problem under consideration as well as at a numerical work. Approximate
expressions for strong or weak fields, compared with the critical field, have
been found. Depending on the ratio of these fields we consider the pure quantum
region of photon energy, where particles are created on lower Landau levels or
created not at all. Also the energy region of large level numbers is considered
where the quasiclassical approximation is valid. | Singularities and Gauge Theory Phases II: We present a simple algebraic construction of all the small resolutions for
the SU(5) Weierstrass model. Each resolution corresponds to a subchamber on the
Coulomb branch of the five-dimensional N=1 SU(5) gauge theory with matter
fields in the fundamental and two-index antisymmetric representations. This
construction unifies all previous resolutions found in the literature in a
single framework. |
Islands in Closed and Open Universes: We show that spatial curvature has a significant effect on the existence of
entanglement islands in cosmology. We consider a homogeneous, isotropic
universe with thermal radiation purified by a reference spacetime. Arbitrarily
small positive curvature guarantees that the entire universe is an island.
Proper subsets of the time-symmetric slice of a closed or open universe can be
islands, but only if the cosmological constant is negative and sufficiently
large in magnitude. | Rayleigh-Schrödinger Perturbation Theory Based on Gaussian
Wavefunctional Approch: A Rayleigh-Schr\"{o}dinger perturbation theory based on the Gaussian
wavefunctional is constructed. The method can be used for calculating the
energies of both the vacuum and the excited states. A model calculation is
carried out for the vacuum state of the $\lambda\phi^4$ field theory. |
Domain Lines as Fractional Strings: We consider N=2 supersymmetric quantum electrodynamics (SQED) with 2 flavors,
the Fayet--Iliopoulos parameter, and a mass term $\beta$ which breaks the
extended supersymmetry down to N=1. The bulk theory has two vacua; at $\beta=0$
the BPS-saturated domain wall interpolating between them has a moduli space
parameterized by a U(1) phase $\sigma$ which can be promoted to a scalar field
in the effective low-energy theory on the wall world-volume. At small
nonvanishing $\beta$ this field gets a sine-Gordon potential. As a result, only
two discrete degenerate BPS domain walls survive. We find an explicit solitonic
solution for domain lines -- string-like objects living on the surface of the
domain wall which separate wall I from wall II. The domain line is seen as a
BPS kink in the world-volume effective theory. We expect that the wall with the
domain line on it saturates both the $\{1,0\}$ and the $\{{1/2},{1/2}\}$b
central charges of the bulk theory. The domain line carries the magnetic flux
which is exactly 1/2 of the flux carried by the flux tube living in the bulk on
each side of the wall. Thus, the domain lines on the wall confine charges
living on the wall, resembling Polyakov's three-dimensional confinement. | P-adic AdS/CFT on subspaces of the Bruhat-Tits tree: On two different subspaces of Bruhat-Tits tree, the exact effective actions
and two-point functions of deformed CFTs are calculated according to the p-adic
version of AdS/CFT. These subspaces are specially chosen such that in the case
of $p\equiv3\pmod4$, they can be viewed as a circle and a hyperbola over p-adic
numbers when taken to infinities. It is found that two-point functions of CFTs
depend on chordal distances of the circle and the hyperbola. |
Aspects of quantum integrability for pure spinor superstring in
AdS(5)xS(5): We consider the monodromy matrix for the pure spinor IIB superstring on
$AdS_5\times S^5$ at leading order at strong coupling, in particular its
variation under an infinitesimal and continuous deformation of the contour.
Such variation is equivalent to the insertion of a local operator. Demanding
the BRST-closure for such an operator rules out its existence, implying that
the monodromy matrix remains contour-independent at the first order in
perturbation theory. Furthermore we explicitly compute the field strength
corresponding to the flat connections up to leading order and directly check
that it is free from logarithmic divergences. The absence of anomaly in the
coordinate transformation of the monodromy matrix and the UV-finiteness of the
curvature tensor finally imply the integrability of the pure spinor superstring
at the first order. | The Analysis of Time-Space Translations in Quantum Fields: I discuss the indefinite metrical structure of the time-space translations as
realized in the indefinite inner products for relativistic quantum fields,
familiar in the example of quantum gauge fields. The arising indefinite unitary
nondiagonalizable representations of the translations suggest as the positive
unitarity condition for the probability interpretable positive definite
asymptotic particle state space the requirement of a vanishing nilpotent part
in the time-space translations realization. A trivial Becchi-Rouet-Stora charge
(classical gauge invariance) for the asymptotics in quantum gauge theories can
be interpreted as one special case of this general principle - the asymptotic
projection to the eigenstates of the time-space translations. |
A Non-relativistic Logarithmic Conformal Field Theory from a Holographic
Point of View: We study a fourth-order derivative scalar field configuration in a fixed
Lifshitz background. Using an auxiliary field we rewrite the equations of
motion as two coupled second order equations. We specialize to the limit that
the mass of the scalar field degenerates with that of the auxiliary field and
show that logarithmic modes appear. Using non-relativistic holographic methods
we calculate the two-point correlation functions of the boundary operators in
this limit and find evidence for a non-relativistic logarithmic conformal field
theory at the boundary. | One-Dimensional Super Calabi-Yau Manifolds and their Mirrors: We apply a definition of generalised super Calabi-Yau variety (SCY) to
supermanifolds of complex dimension one. One of our results is that there are
two SCY's having reduced manifold equal to $\mathbb{P}^1$, namely the
projective super space $\mathbb{P}^{1|2} $ and the weighted projective super
space $\mathbb{WP}^{1|1}_{(2)}$. Then we compute the corresponding sheaf
cohomology of superforms, showing that the cohomology with picture number one
is infinite dimensional, while the de Rham cohomology, which is what matters
from a physical point of view, remains finite dimensional. Moreover, we provide
the complete real and holomorphic de Rham cohomology for generic projective
super spaces $\mathbb P^{n|m}$. We also determine the automorphism groups:
these always match the dimension of the projective super group with the only
exception of $\mathbb{P}^{1|2} $, whose automorphism group turns out to be
larger than the projective general linear supergroup. By considering the
cohomology of the super tangent sheaf, we compute the deformations of
$\mathbb{P}^{1|m}$, discovering that the presence of a fermionic structure
allows for deformations even if the reduced manifold is rigid. Finally, we show
that $\mathbb{P}^{1|2} $ is self-mirror, whereas $\mathbb{WP} ^{1|1}_{(2)}$ has
a zero dimensional mirror. Also, the mirror map for $\mathbb{P}^{1|2}$
naturally endows it with a structure of $N=2$ super Riemann surface. |
Loop Algebra Moment Maps and Hamiltonian Models for the Painleve
Transcendants: The isomonodromic deformations underlying the Painlev\'e transcendants are
interpreted as nonautonomous Hamiltonian systems in the dual $\gR^*$ of a loop
algebra $\tilde\grg$ in the classical $R$-matrix framework. It is shown how
canonical coordinates on symplectic vector spaces of dimensions four or six
parametrize certain rational coadjoint orbits in $\gR^*$ via a moment map
embedding. The Hamiltonians underlying the Painlev\'e transcendants are
obtained by pulling back elements of the ring of spectral invariants. These are
shown to determine simple Hamiltonian systems within the underlying symplectic
vector space. | Nonabelian Bosonic Currents in Cosmic Strings: A nonabelian generalization of the neutral Witten current-carrying string
model is discussed in which the bosonic current-carrier belongs to a two
dimensional representation of SU(2). We find that the current-carrying
solutions can be of three different kinds: either the current spans a U(1)
subgroup, and in which case one is left with an abelian current-carrying
string, or the three currents are all lightlike, travelling in the same
direction (only left or right movers). The third, genuinely nonabelian
situation, cannot be handled within a cylindrically symmetric framework, but
can be shown to depend on all possible string Lorentz invariant quantities that
can be constructed out of the phase gradients. |
Five-dimensional rotating black holes in Einstein-Gauss-Bonnet theory: We present arguments for the existence of five-dimensional rotating black
holes with equal magnitude angular momenta in Einstein-Gauss-Bonnet theory with
negative cosmological constant. These solutions posses a regular horizon of
spherical topology and approach asymptotically an Anti-de Sitter spacetime
background. We discuss the general properties of these solutions and, using an
adapted counterterm prescription, we compute their entropy and conserved
charges. | Baryonic torii: Toroidal baryons in a generalized Skyrme model: We study a Skyrme-type model with a potential term motivated by Bose-Einstein
condensates (BECs), which we call the BEC Skyrme model. We consider two flavors
of the model, the first is the Skyrme model and the second has a sixth-order
derivative term instead of the Skyrme term; both with the added BEC-motivated
potential. The model contains toroidally shaped Skyrmions and they are
characterized by two integers P and Q, representing the winding numbers of two
complex scalar fields along the toroidal and poloidal cycles of the torus,
respectively. The baryon number is B=PQ. We find stable Skyrmion solutions for
P=1,2,3,4,5 with Q=1, while for P=6 and Q=1 it is only metastable. We further
find that configurations with higher Q>1 are all unstable and split into Q
configurations with Q=1. Finally we discover a phase transition, possibly of
first order, in the mass parameter of the potential under study. |
Entanglement Islands in Generalized Two-dimensional Dilaton Black Holes: The Fabbri-Russo model is a generalized model of a two-dimensional dilaton
gravity theory with various parameters "$n$" describing various specific
gravities. Particularly, the Russo-Susskind-Thorlacius gravity model fits the
case $n=1$. In the Fabbri-Russo model, we investigate Page curves and the
entanglement island. Islands are considered in eternal and evaporating black
holes. Surprisingly, in any black hole, the emergence of islands causes the
rise of the entanglement entropy of the radiation to decelerate after the Page
time, satisfying the principle of unitarity. For eternal black holes, the
fine-grained entropy reaches a saturation value that is twice the
Bekenstein-Hawking entropy. For evaporating black holes, the fine-grained
entropy finally reaches zero. The parameter "$n$" significantly impacts the
Page curve at extremely early times. However, at late times and large distance
limit, the impact of the parameter "$n$" is a subleading term and is
exponentially suppressed. As a result, the shape of Page curves is
"$n$"-independent in the leading order. Furthermore, we discuss the
relationship between islands and firewalls. We show that the island is a better
candidate than firewalls for encountering the quantum entanglement-monogamy
problem. Finally, we briefly review the gravity/ensemble duality as a potential
resolution to the state conundrum resulting from the island formula. | Fermion localization in a backreacted warped spacetime: We consider a five dimensional AdS warped spacetime in presence of a massive
scalar field in the bulk. The scalar field potential fulfills the requirement
of modulus stabilization even when the effect of backreaction of the
stabilizing field is taken into account. In such a scenario, we explore the
role of backreaction on the localization of bulk fermions which in turn
determines the effective radion-fermion coupling on the brane. Our result
reveals that both the chiral modes of the zeroth Kaluza-Klein (KK) fermions get
localized near TeV brane as the backreaction of the scalar field increases. We
also show that the profile of massive KK fermions shifts towards the Planck
brane with increasing backreaction parameter. |
Topology change in ISO(2,1) Chern-Simons gravity: In 2+1 dimensional gravity, a dreibein and the compatible spin connection can
represent a space-time containing a closed spacelike surface $\Sigma$ only if
the associated SO(2,1) bundle restricted to $\Sigma$ has the same
non-triviality (Euler class) as that of the tangent bundle of $\Sigma.$ We
impose this bundle condition on each external state of Witten's
topology-changing amplitude. The amplitude is non-vanishing only if the
combination of the space topologies satisfies a certain selection rule. We
construct a family of transition paths which reproduce all the allowed
combinations of genus $g \ge 2$ spaces. | Life-time of Metastable Vacuum in String Theory and Trans-Planckian
Censorship Conjecture: It has been known that the catalytic effect makes the life-time of a
metastable state shorter. We discuss this phenomenon in a decay process of a
metastable vacuum in the brane-limit of type IIB string theory. Due to the
non-linear effect of DBI action, the bubble created by the decay makes an
energetically favorable bound state with an impurity that plays the role of
catalyst, which is quite specific to this model and different from other
catalysts such as a back hole. Furthermore, we found that this low-energy
effective theory around almost unstable regions reduces to a simple quantum
mechanical system, and the vacuum life-time can be calculated using known
results, even beyond the WKB approximation. Finally, we compare the life-time
of the vacuum with the Trans-Planckian Censorship Conjecture (TCC) and find
that as long as the string scale is at least one order magnitude smaller than
the Planck scale, there is a nonzero window to satisfy the TCC condition. |
Supercurrents on Asymmetric Orbifolds: We study $E_8 \times E_8$-heterotic string on asymmetric orbifolds associated
with semi-simple simply-laced Lie algebras. Using the fact that $E_6$-model
allows different twists, we present a new N=1 space-time supersymmetric model
whose supercurrent appears from twisted sectors but not untwisted sector. | The Heterotic Enhancon: The enhancon mechanism is studied in the heterotic string theory. We consider
the N_L=0 winding strings with momentum (NS1-W*) and the Kaluza-Klein dyons
(KK5-NS5*). The NS1-W* and KK5-NS5* systems are dualized to the D4-D0* and
D6-D2* systems, respectively, under the d=6 heterotic/IIA S-duality. The
heterotic form has a number of advantages over the type IIA form. We study
these backgrounds and obtain the enhancon radii by brane probe analysis. The
results are consistent with S-duality. |
THE HIGGS-YUKAWA MODEL IN CURVED SPACETIME: The Higgs-Yukawa model in curved spacetime (renormalizable in the usual
sense) is considered near the critical point, employing the $1/N$--expansion
and renormalization group techniques. By making use of the equivalence of this
model with the standard NJL model, the effective potential in the linear
curvature approach is calculated and the dynamically generated fermionic mass
is found. A numerical study of chiral symmetry breaking by curvature effects is
presented. | Symmetry in noncommutative quantum mechanics: We reconsider the generalization of standard quantum mechanics in which the
position operators do not commute. We argue that the standard formalism found
in the literature leads to theories that do not share the symmetries present in
the corresponding commutative system. We propose a general prescription to
specify a Hamiltonian in the noncommutative theory that preserves the existing
symmetries. We show that it is always possible to choose this Hamiltonian in
such a way that the energy spectrum of the standard and non-commuting theories
are identical, so that experimental differences between the predictions of both
theories are to be found only at the level of the detailed structure of the
energy eigenstates. |
The Noncommutative Supersymmetric Nonlinear Sigma Model: We show that the noncommutativity of space-time destroys the
renormalizability of the 1/N expansion of the O(N) Gross-Neveu model. A similar
statement holds for the noncommutative nonlinear sigma model. However, we show
that, up to the subleading order in 1/N expansion, the noncommutative
supersymmetric O(N) nonlinear sigma model becomes renormalizable in D=3. We
also show that dynamical mass generation is restored and there is no
catastrophic UV/IR mixing. Unlike the commutative case, we find that the
Lagrange multiplier fields, which enforce the supersymmetric constraints, are
also renormalized. For D=2 the divergence of the four point function of the
basic scalar field, which in D=3 is absent, cannot be eliminated by means of a
counterterm having the structure of a Moyal product. | SU(3) x SU(2) x U(1) Vacua in F-Theory: The Standard Model group and matter spectrum is obtained in vacua of
F-theory, without resorting to an intermediate unification group. The group
SU(3) x SU(2) x U(1)_Y is the commutant to SU(5)_t \times U(1)_Y structure
group of a Higgs bundle in E_8 and is geometrically realized as a deformation
of I_5 singularity. Lying along the unification groups of E_n, our vacua
naturally inherit their unification structure. By modding SU(5)_t out by Z_4
monodromy group, we can distinguish Higgses from lepton doublets by matter
parity. Turning on universal G-flux on this part, the spectrum contains three
generations of quarks and leptons, as well as vectorlike pairs of electroweak
and colored Higgses. Minimal Yukawa couplings is obtained at the renormalizable
level. |
Chiral Gauge Dynamics: Candidates for Non-Supersymmetric Dualities: We study the dynamics of chiral SU(N) gauge theories. These contain Weyl
fermions in the symmetric or anti-symmetric representation of the gauge group,
together with further fermions in the fundamental and anti-fundamental. We
revisit an old proposal of Bars and Yankielowicz who match the 't Hooft
anomalies of this theory to free fermions. We show that there are novel and, in
some cases, quite powerful constraints on the dynamics in the large N limit.
In addition, we study these SU(N) theories with an extra Weyl fermion
transforming in the adjoint representation. Here we show that all 21 't Hooft
anomalies for global symmetries are matched with those of a Spin(8) gauge
theory. This suggests a non-supersymmetric extension of the duality of Pouliot
and Strassler. Finally, we also discuss some non-supersymmetric dualities with
vector-like matter content for SO(N) and Sp(N) gauge theories and the
constraints imposed by Weingarten inequalities. | WDVV Equations from Algebra of Forms: A class of solutions to the WDVV equations is provided by period matrices of
hyperelliptic Riemann surfaces, with or without punctures. The equations
themselves reflect associativity of explicitly described multiplicative algebra
of (possibly meromorphic) 1-differentials, which holds at least in the
hyperelliptic case. This construction is direct generalization of the old one,
involving the ring of polynomials factorized over an ideal, and is inspired by
the study of the Seiberg-Witten theory. It has potential to be further extended
to reveal algebraic structures underlying the theory of quantum cohomologies
and the prepotentials in string models with N=2 supersymmetry. |
Electric-magnetic duality as a quantum operator and more symmetries of
$U(1)$ gauge theory: We promote the Noether charge of the electric-magnetic duality symmetry of
$U(1)$ gauge theory, "$G$" to a quantum operator. We construct ladder
operators, $D_{(\pm)a}^\dagger(k)$ and $D_{(\pm)a}(k)$ which create and
annihilate the simultaneous quantum eigen states of the quantum Hamiltonian(or
number) and the electric-magnetic duality operators respectively. Therefore all
the quantum states of the $U(1)$ gauge fields can be expressed by a form of
$|E,g\rangle$, where $E$ is the energy of the state, the $g$ is the eigen value
of the quantum operator $G$, where the $g$ is quantized in the unit of 1. We
also show that 10 independent bilinears comprised of the creation and
annihilation operators can form $SO(2,3)$ which is as demonstrated in the
Dirac's paper published in 1962. The number operator and the electric-magnetic
duality operator are the members of the $SO(2,3)$ generators. We note that
there are two more generators which commute with the number operator(or
Hamiltonian). We prove that these generators are indeed symmetries of the
$U(1)$ gauge field theory action. | A Note on Letters of Yangian Invariants: Motivated by reformulating Yangian invariants in planar ${\cal N}=4$ SYM
directly as $d\log$ forms on momentum-twistor space, we propose a purely
algebraic problem of determining the arguments of the $d\log$'s, which we call
"letters", for any Yangian invariant. These are functions of momentum twistors
$Z$'s, given by the positive coordinates $\alpha$'s of parametrizations of the
matrix $C(\alpha)$, evaluated on the support of polynomial equations $C(\alpha)
\cdot Z=0$. We provide evidence that the letters of Yangian invariants are
related to the cluster algebra of Grassmannian $G(4,n)$, which is relevant for
the symbol alphabet of $n$-point scattering amplitudes. For $n=6,7$, the
collection of letters for all Yangian invariants contains the cluster ${\cal
A}$ coordinates of $G(4,n)$. We determine algebraic letters of Yangian
invariant associated with any "four-mass" box, which for $n=8$ reproduce the
$18$ multiplicative-independent, algebraic symbol letters discovered recently
for two-loop amplitudes. |
Analytic and numerical bootstrap for the long-range Ising model: We combine perturbation theory with analytic and numerical bootstrap
techniques to study the critical point of the long-range Ising (LRI) model in
two and three dimensions. This model interpolates between short-range Ising
(SRI) and mean-field behaviour. We use the Lorentzian inversion formula to
compute infinitely many three-loop corrections in the two-dimensional LRI near
the mean-field end. We further exploit the exact OPE relations that follow from
bulk locality of the LRI to compute infinitely many two-loop corrections near
the mean-field end, as well as some one-loop corrections near SRI. By including
such exact OPE relations in the crossing equations for LRI we set up a very
constrained bootstrap problem, which we solve numerically using SDPB. We find a
family of sharp kinks for two- and three-dimensional theories which compare
favourably to perturbative predictions, as well as some Monte Carlo simulations
for the two-dimensional LRI. | Coupling Constants in Asymptotic Expansions: Perturbation theory is a powerful tool in manipulating dynamical system.
However, it is legal only for infinitesimal perturbations. We propose to
dispose this problem by means of perturbation group, and find that the coupling
constant approaches to zero in the limit of high order perturbations as Dyson
once expected. |
Holographic Gas as Dark Energy: We investigate the statistical nature of holographic gas, which may represent
the quasi-particle excitations of a strongly correlated gravitational system.
We find that the holographic entropy can be obtained by modifying degeneracy.
We calculate thermodynamical quantities and investigate stability of the
holographic gas. When applying to cosmology, we find that the holographic gas
behaves as holographic dark energy, and the parameter $c$ in holographic dark
energy can be calculated from our model. Our model of holographic gas generally
predicts $c<1$, implying that the fate of our universe is phantom like. | Bulk versus brane running couplings: A simplified higher dimensional Randall-Sundrum-like model in 6 dimensions is
considered. It has been observed previously by Goldberger and Wise that in such
a self-interacting scalar theory on the bulk with a conical singularity there
is mixing of renormalization of 4d brane couplings with that of the bulk
couplings. We study the influence of the running bulk couplings on the running
of the 4d brane couplings. We find that bulk quantum effects may completely
alter the running of brane couplings. In particular, the structure of the
Landau pole may be drastically altered and non-asymptotically free running may
turn into asymptotically safe (or free) behavior. |
Canonical quantization approach to 2d gravity coupled to c<1 matter: We show that all important features of 2d gravity coupled to $c<1$ matter can
be easily understood from the canonical quantization approach a la Dirac.
Furthermore, we construct a canonical transformation which maps the theory into
a free-field form, i.e. the constraints become free-field Virasoro generators
with background charges. This implies the gauge independence of the
David-Distler-Kawai results, and also proves the free-field assumption which
was used for obtaining the spectrum of the theory in the conformal gauge. A
discussion of the unitarity of the physical spectrum is presented and we point
out that the scalar products of the discrete states are not well defined in the
standard Fock space framework. | Nonlinear Constraints on Relativistic Fluids Far From Equilibrium: New constraints are found that must necessarily hold for Israel-Stewart-like
theories of fluid dynamics to be causal far away from equilibrium. Conditions
that are sufficient to ensure causality, local existence, and uniqueness of
solutions in these theories are also presented. Our results hold in the full
nonlinear regime, taking into account bulk and shear viscosities (at zero
chemical potential), without any simplifying symmetry or near-equilibrium
assumptions. Our findings provide fundamental constraints on the magnitude of
viscous corrections in fluid dynamics far from equilibrium. |
5D Differential Calculus and Noether Analysis of Translation Symmetries
in kappa-Minkowski Noncommutative Spacetime: We perform a Noether analysis for a description of translation
transformations in 4D kappa-Minkowski noncommutative spacetime which is based
on the structure of a 5D differential calculus. Taking properly into account
the properties of the differential calculus we arrive at an explicit formula
for the conserved charges. We also propose a choice of basis for the 5D
calculus which leads to an intuitive description of time derivatives. | Diffeomorphism Symmetry in Two Dimensions and Celestial Holography: Two-dimensional diffeomorphism symmetry can be described by an operator
algebra extension of the well-known Virasoro algebra description of conformal
symmetry. Utilizing this extension, this note explains why the conformal
symmetry that appears in celestial holography should not be extended to
diffeomorphism symmetry, a possibility that several authors have proposed. The
description of the two-dimensional diffeomorphism algebra presented here might
be useful for other purposes. |
On the Thermodynamics of Large N Noncommutative Super Yang-Mills Theory: We study the thermodynamics of the large N noncommutative super Yang-Mills
theory in the strong 't Hooft coupling limit in the spirit of AdS/CFT
correspondence. It has already been noticed that some thermodynamic quantities
of near-extremal D3-branes with NS B fields, which are dual gravity
configurations of the noncommutative ${\cal N}$=4 super Yang-Mills theory, are
the same as those without B fields. In this paper, (1) we examine the
$\alpha'^3 R^4$ corrections to the free energy and find that the part of the
tree-level contribution remains unchanged, but the one-loop and the
non-perturbative D-instanton corrections are suppressed, compared to the
ordinary case. (2) We consider the thermodynamics of a bound state probe
consisting of D3-branes and D-strings in the near-extremal D3-brane background
with B field, and find the thermodynamics of the probe is the same as that of a
D3-brane probe in the D3-brane background without B field. (3) The
stress-energy tensor of the noncommutative super Yang-Mills theory is
calculated via the AdS/CFT correspondence. It is found that the tensor is not
isotropic and its trace does not vanish, which confirms that the super
Yang-Mills is not conformal even in four dimensions due to the noncommutative
nature of space. Our results render further evidence for the argument that the
large N noncommutative and ordinary super Yang-Mills theories are equivalent
not only in the weak coupling limit, but also in the strong coupling limit. | Unifying the 6D $\mathcal{N}=(1,1)$ String Landscape: We propose an organizing principle for string theory moduli spaces in six
dimensions with $\mathcal{N} = (1,1)$, based on a rank reduction map, into
which all known constructions fit. In the case of cyclic orbifolds, which are
the main focus of the paper, we make an explicit connection with meromorphic 2D
(s)CFTs with $c = 24$ ($c = 12$) and show how these encode every possible gauge
symmetry enhancement in their associated 6D theories. These results generalize
naturally to non-cyclic orbifolds, into which the only known string
construction (to our awareness) also fits. This framework suggests the
existence of a total of 47 moduli spaces: the Narain moduli space, 23 of cyclic
orbifold type and 23 of non-cyclic type. Of these only 17 have known string
constructions. Among the 30 new moduli spaces, 15 correspond to pure
supergravity, for a total of 16 such spaces. A full classification of
nonabelian gauge symmetries is given, and as a byproduct we complete the one
for seven dimensions, in which only those of theories with heterotic
descriptions were known exhaustively. |
On the Possibility of Super-luminal Propagation in a Gravitational
Background: We argue that superluminal propagation in a gravitational field discovered by
Drummond and Hathrell in the lowest order of perturbation theory remains intact
in higher orders. The criticism of this result based on an exact calculation of
the one loop correction to the photon polarization operator in the Penrose
plane wave approximation is not tenable. The statement that quantum causality
is automatically imposed by classical causality is possibly invalid due to the
infrared nature of the same triangle diagram which also contributes to the
quantum trace anomaly. | The Dirichlet Casimir Energy for $φ^4$ Theory in a Rectangle: In this article, we present the zero and first-order radiative correction to
the Dirichlet Casimir energy for massive and massless scalar field confined in
a rectangle. This calculation procedure was conducted in two spatial dimensions
and for the case of the first-order correction term is new. The renormalization
program that we have used in this work, allows all influences from the dominant
boundary conditions (e.g. the Dirichlet boundary condition) be automatically
reflected in the counterterms. This permission usually makes the counterterms
position-dependent. Along with the renormalization program, a supplementary
regularization technique was performed in this work. In this regularization
technique, that we have named Box Subtraction Scheme (BSS), two similar
configurations were introduced and the zero point energies of these two
configurations were subtracted from each other using appropriate limits. This
regularization procedure makes the usage of any analytic continuation
techniques unnecessary. In the present work, first, we briefly present
calculation of the leading order Casimir energy for the massive scalar field in
a rectangle via BSS. Next, the first order correction to the Casimir energy is
calculated by applying the mentioned renormalization and regularization
procedures. Finally, all the necessary limits of obtained answers for both
massive and massless cases are discussed. |
From Quantum Probabilities to Classical Facts: Model interactions between classical and quantum systems are briefly
reviewed. These include: general measurement - like couplings, Stern-Gerlach
experiment, model of a counter, quantum Zeno effect, piecewise deterministic
Markov processes and meaning of the wave function. | Boundary spectrum in the sine-Gordon model with Dirichlet boundary
conditions: We find the spectrum of boundary bound states for the sine-Gordon model with
Dirichlet boundary conditions, closing the bootstrap and providing a complete
description of all the poles in the boundary reflection factors. The boundary
Coleman-Thun mechanism plays an important role in the analysis. Two basic
lemmas are introduced which should hold for any 1+1-dimensional boundary field
theory, allowing the general method to be applied to other models. |
Chern-Simons Theory in SIM(1) Superspace: In this paper, we will analyse a three dimensional supersymmetric
Chern-Simons theory in SIM(1) superspace formalism. The breaking of the Lorentz
symmetry down to the SIM(1) symmetry, breaks half the supersymmetry of the
Lorentz invariant theory. So, the supersymmetry of the Lorentz invariant
Chern-Simons theory with N=1 supersymmetry will break down to N=1/2
supersymmetry, when the Lorentz symmetry is broken down to the SIM(1) symmetry.
First, we will write the Chern-Simons action using SIM(1) projections of N=1
superfields. However, as the SIM(1) transformations of these projections are
very complicated, we will define SIM(1) superfields which transform simply
under SIM(1) transformations. We will then express the Chern-Simons action
using these SIM(1) superfields. Furthermore, we will analyse the gauge symmetry
of this Chern-Simons theory. This is the first time that a Chern-Simons theory
with N=1/2 supersymmetry will be constructed on a manifold without a boundary. | Genus four superstring measures: A main issue in superstring theory are the superstring measures. D'Hoker and
Phong showed that for genus two these reduce to measures on the moduli space of
curves which are determined by modular forms of weight eight and the bosonic
measure. They also suggested a generalisation to higher genus. We showed that
their approach works, with a minor modification, in genus three and we
announced a positive result also in genus four. Here we give the modular form
in genus four explicitly. Recently S. Grushevsky published this result as part
of a more general approach. |
Geometric Actions for D-Branes and M-Branes: New forms of Born-Infeld, D-brane and M theory five-brane actions are found
which are quadratic in the abelian field strength. The gauge fields couple both
to a background or induced metric and a new auxiliary metric, whose elimination
reproduces the non-polynomial Born-Infeld action. This is similar to the
introduction of an auxiliary metric to simplify the Nambu-Goto string action.
This simplifies the quantisation and dualisation of the gauge fields. | Algebraic Renormalization of $N=1$ Supersymmetric Gauge Theories: The complete renormalization procedure of a general N=1 supersymmetric gauge
theory in the Wess-Zumino gauge is presented, using the regulator free
``algebraic renormalization'' procedure. Both gauge invariance and
supersymmetry are included into one single BRS invariance. The form of the
general nonabelian anomaly is given. Furthermore, it is explained how the gauge
BRS and the supersymmetry functional operators can be extracted from the
general BRS operator. It is then shown that the supersymmetry operators
actually belong to the closed, finite, Wess-Zumino superalgebra when their
action is restricted to the space of the ``gauge invariant operators'', i.e. to
the cohomology classes of the gauge BRS operator. An erratum is added at the
end of the paper. |
Review of AdS/CFT Integrability, Chapter V.2: Dual Superconformal
Symmetry: Scattering amplitudes in planar N=4 super Yang-Mills theory reveal a
remarkable symmetry structure. In addition to the superconformal symmetry of
the Lagrangian of the theory, the planar amplitudes exhibit a dual
superconformal symmetry. The presence of this additional symmetry imposes
strong restrictions on the amplitudes and is connected to a duality relating
scattering amplitudes to Wilson loops defined on polygonal light-like contours.
The combination of the superconformal and dual superconformal symmetries gives
rise to a Yangian, an algebraic structure which is known to be related to the
appearance of integrability in other regimes of the theory. We discuss two dual
formulations of the symmetry and address the classification of its invariants. | The kappa-(A)dS quantum algebra in (3+1) dimensions: The quantum duality principle is used to obtain explicitly the Poisson
analogue of the kappa-(A)dS quantum algebra in (3+1) dimensions as the
corresponding Poisson-Lie structure on the dual solvable Lie group. The
construction is fully performed in a kinematical basis and deformed Casimir
functions are also explicitly obtained. The cosmological constant $\Lambda$ is
included as a Poisson-Lie group contraction parameter, and the limit
$\Lambda\to 0$ leads to the well-known kappa-Poincar\'e algebra in the
bicrossproduct basis. A twisted version with Drinfel'd double structure of this
kappa-(A)dS deformation is sketched. |
Field Decomposition and the Ground State Structure of SU(2) Yang-Mills
Theory: We compute the effective potential of SU(2) Yang-Mills theory using the
background field method and the Faddeev-Niemi decomposition of the gauge
fields. In particular, we find that the potential will depend on the values of
two scalar fields in the decomposition and that its structure will give rise to
a symmetry breaking. | Gravity with linear action and gravitational singularities: Motivated by quantum mechanical considerations we earlier suggested an
alternative action for discretised quantum gravity which has a dimension of
length. It is the so called "linear" action. The proposed action is a "square
root" of the classical area action in gravity and has in front of the action a
new constant of dimension one. Here we shall consider the continuous limit of
the discretised linear action. We shall demonstrate that in the modified theory
of gravity there appear space-time regions of the Schwarzschild radius scale
which are unreachable by test particles. These regions are located in the
places where standard theory of gravity has singularities. We are confronted
here with a drastically new concept that there may exist space-time regions
which are excluded from the physical scene, being physically unreachable by
test particles or observables. If this concept is accepted, then it seems
plausible that the gravitational singularities are excluded from the modified
theory. |
Bulk gauge and matter fields in nested warping: I. the formalism: The lack of evidence for a TeV-mass graviton has been construed as
constricting the Randall-Sundrum model. However, a doubly-warped generalization
naturally avoids such restrictions. We develop, here, the formalism for
extension of the Standard Model gauge bosons and fermions into such a
six-dimensional bulk. Apart from ameliorating the usual problems such as
flavour-changing neutral currents, this model admits two very distinct phases,
with their own unique phenomenologies. | Twisted K-Theory as a BRST Cohomology: We use the BRST formalism to classify the gauge orbits of type II string
theory's Ramond-Ramond (RR) field strengths under large RR gauge
transformations of the RR gauge potentials. We find that this construction is
identical to the Atiyah-Hirzebruch spectral sequence construction of twisted
K-theory, where the Atiyah-Hirzebruch differentials are the BRST operators. The
actions of the large gauge transformations on the field strengths that lie in
an integral lattice of de Rham cohomology are found using supergravity, while
the action on Z_2 torsion classes is found using the Freed-Witten anomaly. We
speculate that an S-duality covariant classification may be obtained by
including NSNS gauge transformations and using the BV formalism. An example of
a Z_3 torsion generalization of the Freed-Witten anomaly is provided. |
Holographic Complexity of Rotating Quantum Black Holes: We study holographic complexity for the rotating quantum BTZ black holes
(quBTZ), the BTZ black holes with corrections from bulk quantum fields. Using
double holography, the combined system of backreacted rotating BTZ black holes
with conformal matters, can be holographically described by the rotating AdS4
C-metric with the BTZ black hole living on a codimension-1 brane. We
investigate both volume complexity and action complexity of rotating quBTZ, and
pay special attention to their late-time behaviors. When the mass of BTZ black
hole is not very small and the rotation is not very slow, we show that the
late-time rates of the volume complexity and the action complexity agree with
each other up to a factor 2 and reduce to the ones of BTZ at the leading
classical order, and they both receive subleading quantum corrections. For the
volume complexity, the leading quantum correction comes from the backreaction
of comformal matter on the geometry, similar to the static quBTZ case. For the
action complexity, unlike the static case, the Wheeler-de Witt (WdW) patch in
computing the action complexity for the rotating black hole does not touch the
black hole singularity such that the leading order result is in good match with
the one of classical BTZ. However, when the mass of BTZ black hole is small or
the rotation parameter a is small, the quantum correction to the action
complexity could be significant such that the late-time slope of the action
complexity of quBTZ deviates very much from the one of classical BTZ.
Remarkably, we notice that the nonrotating limit $a \to 0$ is singular and does
not lead to the late-time slope of the action complexity for non-rotating
quantum BTZ black hole. The similar phenomenon happens for higher dimensional
rotating black holes. | Superconformal Symmetry, The Supercurrent And Non-BPS Brane Dynamics: The Noether currents associated with the non-linearly realized
super-Poincare' symmetries of the Green-Schwarz (Nambu-Goto-Akulov-Volkov)
action for a non-BPS p=2 brane embedded in a N=1, D=4 target superspace are
constructed. The R symmetry current, the supersymmetry currents, the
energy-momentum tensor and the scalar central charge current are shown to be
components of a world volume supercurrent. The centrally extended
superconformal transformations are realized on the Nambu-Goldstone boson and
fermion fields of the non-BPS brane. The superconformal currents form
supersymmetry multiplets with the world volume conformal central charge current
and special conformal current being the primary components of the supersymmetry
multiplets containing all the currents. Correspondingly the superconformal
symmetry breaking terms form supersymmetry multiplets the components of which
are obtainable as supersymmetry transformations of the primary currents'
symmetry breaking terms. |
More on the Similarity between D=5 Simple Supergravity and M Theory: It has been known that D=5 simple supergravity resembles D=11 supergravity in
many respects. We present their further resemblances in (1) the duality groups
upon dimensional reduction, and (2) the worldsheet structure of the solitonic
string of the D=5 supergravity. We show that the D=3, G_{2(+2)}/SO(4) (bosonic)
nonlinear sigma model is obtained by using Freudenthal's construction in
parallel to the derivation of the D=3, E_{8(+8)}/SO(16) sigma model from D=11
supergravity. The zero modes of the string solution with unbroken (4,0)
supersymmetry consist of three (non-chiral) scalars, four Majorana-Weyl spinors
of the same chirality and one chiral scalar, which suggests a duality to a
certain six-dimensional chiral string theory. The worldsheet gravitational
anomaly indicates a quantum correction to the Bianchi identity for the dualized
two-form gauge field in the bulk just like the M5-brane case. | The effective potential of gauged NJL model in magnetic field: The formalism, which permits to study the phase structure of gauged NJL-model
for arbitrary external fields, is developed. The effective potential in the
gauged NJL model in the weak magnetic field is found. It is shown that in fixed
gauge coupling case the weak magnetic field doesn't influence chiral symmetry
breaking condition. The analogy with the situation near black hole is briefly
mentioned. |
Supersymmetric $AdS_5$ black holes and strings from 5D $N=4$ gauged
supergravity: We study supersymmetric $AdS_3\times \Sigma_2$ and $AdS_2\times \Sigma_3$
solutions, with $\Sigma_2=S^2,H^2$ and $\Sigma_3=S^3,H^3$, in five-dimensional
$N=4$ gauged supergravity coupled to five vector multiplets. The gauge groups
considered here are $U(1)\times SU(2)\times SU(2)$, $U(1)\times SO(3,1)$ and
$U(1)\times SL(3,\mathbb{R})$. For $U(1)\times SU(2)\times SU(2)$ gauge group
admiting two supersymmetric $N=4$ $AdS_5$ vacua, we identify a new class of
$AdS_3\times \Sigma_2$ and $AdS_2\times H^3$ solutions preserving four
supercharges. Holographic RG flows describing twisted compactifications of
$N=2$ four-dimensional SCFTs dual to the $AdS_5$ vacua to the SCFTs in two and
one dimensions dual to these geometries are numerically given. The solutions
can also be interpreted as supersymmetric black strings and black holes in
asymptotically $AdS_5$ spaces with near horizon geometries given by
$AdS_3\times \Sigma_2$ and $AdS_2\times H^3$, respectively. These solutions
broaden previously known black brane solutions including half-supersymmetric
$AdS_5$ black strings recently found in $N=4$ gauged supergravity. Similar
solutions are also studied in non-compact gauge groups $U(1)\times SO(3,1)$ and
$U(1)\times SL(3,\mathbb{R})$. | Superspace formulation of the Chern character of a theta-summable
Fredholm module: We apply the concepts of superanalysis to present an intrinsically
supersymmetric formulation of the Chern character in entire cyclic cohomology.
We show that the cocycle condition is closely related to the invariance under
supertranslations. Using the formalism of superfields, we find a path integral
representation of the index of the generalized Dirac operator. |
Critical points of WAdS/CFT and higher-curvature gravity: WAdS/WCFT correspondence is an interesting realization of non-AdS holography.
It relates 3-dimensional Warped-Anti-de Sitter (WAdS$_3$) spaces to a special
class of 2-dimensional quantum field theory with chiral scaling symmetry that
acts only on right-moving modes. The latter are often called Warped Conformal
Field Theories (WCFT$_2$), and their existence makes WAdS/WCFT particularly
interesting as a tool to investigate a new type of 2-dimensional conformal
structure. Besides, WAdS/WCFT is interesting because it enables to apply
holographic techniques to the microstate counting problem of non-AdS,
non-supersymmetric black holes. Asymptotically WAdS$_3$ black holes (WBH$_3$)
appear as solutions of topologically massive theories, Chern-Simons theories,
and many other models. Here, we explore WBH$_3\times \Sigma_{D-3}$ solutions of
$D$-dimensional higher-curvature gravity, with $\Sigma_{D-3}$ being different
internal manifolds, typically given by products of deformations of hyperbolic
spaces, although we also consider warped products with time-dependent
deformations. These geometries are solutions of the second order
higher-curvature theory at special (critical) points of the parameter space,
where the theory exhibits a sort of degeneracy. We argue that the dual (W)CFT
at those points is actually trivial. In many respects, these critical points of
WAdS$_3 \times \Sigma_{D-3}$ vacua are the squashed/stretched analogs of the
AdS$_D$ Chern-Simons point of Lovelock gravity. | Pre-Big Bang Scenario on Self-T-Dual Bouncing Branes: We consider a new class of 5-dimensional dilatonic actions which are
invariant under T-duality transformations along three compact coordinates,
provided that an appropriate potential is chosen. We show that the invariance
remains when we add a boundary term corresponding to a moving 3-brane, and we
study the effects of the T-duality symmetry on the brane cosmological
equations. We find that T-duality transformations in the bulk induce scale
factor duality on the brane, together with a change of sign of the pressure of
the brane cosmological matter. However, in a remarkable analogy with the
Pre-Big Bang scenario, the cosmological equations are unchanged. Finally, we
propose a model where the dual phases are connected through a scattering of the
brane induced by an effective potential. We show how this model can realise a
smooth, non-singular transition between a pre-Big Bang superinflationary
Universe and a post-Big Bang accelerating Universe. |
Comment on "What the information loss is {\it not}": A recent article by Mathur attempts a "precise formulation" for the paradox
of black hole information loss [S. D. Mathur, arXiv:1108.0302v2 (hep-th)]. We
point out that a key component of the above work, which refers to entangled
pairs inside and outside of the horizon and their associated entropy gain or
information loss during black hole evaporation, is a presumptuous false outcome
not backed by the very foundation of physics. The very foundation of Mathur's
above work is thus incorrect. We further show that within the framework of
Hawking radiation as tunneling the so-called small corrections are sufficient
to resolve the information loss problem. | Conformal Symmetry of a Black Hole as a Scaling Limit: A Black Hole in
an Asymptotically Conical Box: We show that the previously obtained subtracted geometry of four-dimensional
asymptotically flat multi-charged rotating black holes, whose massless wave
equation exhibit $SL(2,\R) \times SL(2,\R) \times SO(3)$ symmetry may be
obtained by a suitable scaling limit of certain asymptotically flat
multi-charged rotating black holes, which is reminiscent of near-extreme black
holes in the dilute gas approximation. The co-homogeneity-two geometry is
supported by a dilation field and two (electric) gauge-field strengths. We also
point out that these subtracted geometries can be obtained as a particular
Harrison transformation of the original black holes. Furthermore the subtracted
metrics are asymptotically conical (AC), like global monopoles, thus describing
"a black hole in an AC box". Finally we account for the the emergence of the
$SL(2,\R) \times SL(2,\R) \times SO(3)$ symmetry as a consequence of the
subtracted metrics being Kaluza-Klein type quotients of $ AdS_3\times 4 S^3$.
We demonstrate that similar properties hold for five-dimensional black holes. |
Theories of Class F and Anomalies: We consider the 6d (2,0) theory on a fibration by genus g curves, and
dimensionally reduce along the fiber to 4d theories with duality defects. This
generalizes class S theories, for which the fibration is trivial. The
non-trivial fibration in the present setup implies that the gauge couplings of
the 4d theory, which are encoded in the complex structures of the curve, vary
and can undergo S-duality transformations. These monodromies occur around 2d
loci in space-time, the duality defects, above which the fiber is singular. The
key role that the fibration plays here motivates refering to this setup as
theories of class F. In the simplest instance this gives rise to 4d N=4
Super-Yang-Mills with space-time dependent coupling that undergoes SL(2, Z)
monodromies. We determine the anomaly polynomial for these theories by pushing
forward the anomaly polynomial of the 6d (2,0) theory along the fiber. This
gives rise to corrections to the anomaly polynomials of 4d N=4 SYM and theories
of class S. For the torus case, this analysis is complemented with a field
theoretic derivation of a U(1) anomaly in 4d N=4 SYM. The corresponding anomaly
polynomial is tested against known expressions of anomalies for wrapped
D3-branes with varying coupling, which are known field theoretically and from
holography. Extensions of the construction to 4d N = 0 and 1, and 2d theories
with varying coupling, are also discussed. | Self-consistent Analytic Solutions in Twisted $\mathbb{C}P^{N-1}$ Model
in the Large-$N$ Limit: We construct self-consistent analytic solutions in the ${\mathbb C}P^{N-1}$
model in the large-$N$ limit, in which more than one Higgs scalar component
take values inside a single or multiple soliton on an infinite space or on a
ring, or around boundaries of a finite interval. |
Generalized symmetries of topological field theories: We study generalized symmetries in a simplified arena in which the usual
quantum field theories of physics are replaced with topological field theories
and the smooth structure with which the symmetry groups of physics are usually
endowed is forgotten. Doing so allows many questions of physical interest to be
answered using the tools of homotopy theory. We study both global and gauge
symmetries, as well as `t Hooft anomalies, which we show fall into one of two
classes. Our approach also allows some insight into earlier work on symmetries
(generalized or not) of topological field theories. | Duality, generalized Chern-Simons terms and gauge transformations in a
high-dimensional curved spacetime: With two typical parent actions we have two kinds of dual worlds: i) one of
which contains an electric as well as magnetic current, and ii) the other
contains (generalized) Chern-Simons terms. All these fields are defined on a
curved spacetime of arbitrary (odd) dimensions. A new form of gauge
transformations is introduced and plays an essential role in defining the
interaction with a magnetic monopole or in defining the generalized
Chern-Simons terms. |
Yang-Mills theories in dimensions 3,4,6,10 and Bar-duality: In this note we give a homological explanation of "pure spinors" in YM
theories with minimal amount of supersymmetries. We construct A_{\infty}
algebras A for every dimension D=3,4,6,10, which for D=10 coincides with
homogeneous coordinate ring of pure spinors with coordinate lambda^{alpha}.
These algebras are Bar-dual to Lie algebras generated by supersymmetries,
written in components. The algebras have a finite number of higher
multiplications. The main result of the present note is that in dimension
D=3,6,10 the algebra A\otimes \Lambda[\theta^{\alpha}]\otimes Mat_n with a
differential D is equivalent to Batalin-Vilkovisky algebra of minimally
supersymmetric YM theory in dimension D reduced to a point. This statement can
be extended to nonreduced theories. | Shifted quantum groups and matter multiplets in supersymmetric gauge
theories: The notion of shifted quantum groups has recently played an important role in
algebraic geometry. This subtle modification of the original definition brings
more flexibility in the representation theory of quantum groups. The first part
of this paper presents new mathematical results for the shifted quantum
toroidal $\mathfrak{gl}(1)$ and quantum affine $\mathfrak{sl}(2)$ algebras
(resp. denoted $\ddot{U}_{q_1,q_2}^\boldsymbol{\mu}(\mathfrak{gl}(1))$ and
$\dot{U}_q^\boldsymbol{\mu}(\mathfrak{sl}(2))$). It defines several new
representations, including finite dimensional highest $\ell$-weight
representations for the toroidal algebra, and a vertex representation of
$\dot{U}_q^\boldsymbol{\mu}(\mathfrak{sl}(2))$ acting on Hall-Littlewood
polynomials. It also explores the relations between representations of
$\dot{U}_q^\boldsymbol{\mu}(\mathfrak{sl}(2))$ and
$\ddot{U}_{q_1,q_2}^\boldsymbol{\mu}(\mathfrak{gl}(1))$ in the limit
$q_1\to\infty$ ($q_2$ fixed), and present the construction of several new
intertwiners. These results are used in the second part to construct BPS
observables for 5d $\mathcal{N}=1$ and 3d $\mathcal{N}=2$ gauge theories. In
particular, it is shown that 5d hypermultiplets and 3d chiral multiplets can be
introduced in the algebraic engineering framework using shifted
representations, and the Higgsing procedure is revisited from this perspective. |
Double-soft behavior for scalars and gluons from string theory: We compute the leading double-soft behavior for gluons and for the scalars
obtained by dimensional reduction of a higher dimensional pure gauge theory,
from the scattering amplitudes of gluons and scalars living in the world-volume
of a Dp-brane of the bosonic string. In the case of gluons, we compute both the
double-soft behavior when the two soft gluons are contiguous as well as when
they are not contiguous. From our results, that are valid in string theory, one
can easily get the double-soft limit in gauge field theory by sending the
string tension to infinity. | The Geometry of Quantum Mechanics: A recent notion in theoretical physics is that not all quantum theories arise
from quantising a classical system. Also, a given quantum model may possess
more than just one classical limit. These facts find strong evidence in string
duality and M-theory, and it has been suggested that they should also have a
counterpart in quantum mechanics. In view of these developments we propose
"dequantisation", a mechanism to render a quantum theory classical.
Specifically, we present a geometric procedure to "dequantise" a given quantum
mechanics (regardless of its classical origin, if any) to possibly different
classical limits, whose quantisation gives back the original quantum theory.
The standard classical limit $\hbar\to 0$ arises as a particular case of our
approach. |
Exact Dynamics of Quantum Dissipative System in Constant External Field: The quantum dynamics of a simplest dissipative system, a particle moving in a
constant external field , is exactly studied by taking into account its
interaction with a bath of Ohmic spectral density. We apply the main idea and
methods developed in our recent work [1] to quantum dissipative system with
constant external field. Quantizing the dissipative system we obtain the simple
and exact solutions for the coordinate operator of the system in Heisenberg
picture and the wave function of the composite system of system and bath in
Schroedinger picture. An effective Hamiltonian for the dissipative system is
explicitly derived from these solutions with Heisenberg picture method and
thereby the meaning of the wavefunction governed by it is clarified by
analyzing the effect of the Brownian motion. Especially, the general effective
Hamiltonian for the case with arbitrary potential is directly derived with this
method for the case when the Brownian motion can be ignored. Using this
effective Hamiltonian, we show an interesting fact that the dissipation
suppresses the wave packet spreading. | Developing the Covariant Batalin-Vilkovisky approach to String Theory: We investigate the variation of the string field action under changes of the
string field vertices giving rise to different decompositions of the moduli
spaces of Riemann surfaces. We establish that any such change in the string
action arises from a field transformation canonical with respect to the
Batalin-Vilkovisky (BV) antibracket, and find the explicit form of the
generator of the infinitesimal transformations. Two theories using different
decompositions of moduli space are shown to yield the same gauge fixed action
upon use of different gauge fixing conditions. We also elaborate on recent work
on the covariant BV formalism, and emphasize the necessity of a measure in the
space of two dimensional field theories in order to extend a recent analysis of
background independence to quantum string field theory. |
Duality Invariance: From M-theory to Double Field Theory: We show how the duality invariant approach to M-theory formulated by Berman
and Perry relates to the double field theory proposed by Hull and Zwiebach. In
doing so we provide suggestions as to how Ramond fields can be incorporated
into the double field theory. We find that the standard dimensional reduction
procedure has a duality invariant (doubled) analogue in which the gauge fields
of the doubled Kaluza-Klein ansatz encode the Ramond potentials. We identify
the internal gauge index of these gauge fields with a spinorial index of
O(d,d). | Covariant Hamilton-Jacobi Equation for Pure Gravity: The main purpose of this article is to provide access to a previously
unpublished and nearly lost paper: P. Ho\v{r}ava, "Covariant Hamilton-Jacobi
Equation for Pure Gravity", which appeared originally in July 1990 as a Prague
Preprint PRA-HEP-90/4, at the Institute of Physics, Czechoslovak Academy of
Sciences, but appears otherwise unavailable online. The author has recently
acquired an original copy of this preprint; the present article contains a
verbatim transcript of the original 1990 paper, framed by a small number of
comments. The contents of the 1990 paper was based on the results contained in
the author's BSc Thesis, written in Czech, and presented at Charles University,
Prague, in 1986.
The original 1990 Abstract: We present an alternative framework for treating
Einstein gravity in any dimension greater than two, and at any signature. It is
based on a covariant Hamilton-Jacobi-De~Donder equation, which is proved to be
equivalent to the Lagrange theory, on space-times of arbitrary topology. It in
particular means that Einstein gravity can be thought of as a (covariantly)
regular system. Finally, the Hamilton-Jacobi theory is studied, and it is shown
that any solution of Einstein equations can be obtained from the action form
equal identically to zero. |
Super D-string Action on $AdS_5 \times S^5$: We present a supersymmetric and $\kappa$-symmetric D-string action on $AdS_5
\times S^5$ in supercoset construction. As in the previous work of the super
D-string action in the flat background, the super D-string action on $AdS_5
\times S^5$ can be transformed to a form of the IIB Green-Schwarz superstring
action with the $SL(2,Z)$ covariant tension on $AdS_5 \times S^5$ through a
duality transformation. In order to understand a part of the duality
transformation as SO(2) rotation of N=2 spinor coordinates, it seems to be
necessary to fix the $\kappa$-symmetry in a gauge condition which simplifies
the classical action. This is the article showing for the first time that there
exists S-duality in type IIB superstring theory in a curved background whose
validity has been conjectured in the past but not shown so far in an explicit
way. | Debye entropic force and modified Newtonian dynamics: Verlinde has suggested that the gravity has an entropic origin, and a
gravitational system could be regarded as a thermodynamical system. It is
well-known that the equipartition law of energy is invalid at very low
temperature. Therefore, entropic force should be modified while the temperature
of the holographic screen is very low. It is shown that the modified entropic
force is proportional to the square of the acceleration, while the temperature
of the holographic screen is much lower than the Debye temperature $T_D$. The
modified entropic force returns to the Newton's law of gravitation while the
temperature of the holographic screen is much higher than the Debye
temperature. The modified entropic force is connected with modified Newtonian
dynamics (MOND). The constant $a_0$ involved in MOND is linear in the Debye
frequency $\omega_D$, which can be regarded as the largest frequency of the
bits in screen. We find that there do have a strong connection between MOND and
cosmology in the framework of Verlinde's entropic force, if the holographic
screen is taken to be bound of the Universe. The Debye frequency is linear in
the Hubble constant $H_0$. |
Towards R-matrix construction of Khovanov-Rozansky polynomials. I.
Primary $T$-deformation of HOMFLY: We elaborate on the simple alternative from arXiv:1308.5759 to the
matrix-factorization construction of Khovanov-Rozansky (KR) polynomials for
arbitrary knots and links in the fundamental representation of arbitrary SL(N).
Construction consists of 2 steps: first, with every link diagram with m
vertices one associates an m-dimensional hypercube with certain q-graded vector
spaces, associated to its 2^m vertices. A generating function for q-dimensions
of these spaces is what we suggest to call the primary T-deformation of HOMFLY
polynomial -- because, as we demonstrate, it can be explicitly reduced to
calculations of ordinary HOMFLY polynomials, i.e. to manipulations with quantum
R-matrices. The second step is a certain minimization of residues of this new
polynomial with respect to T+1. Minimization is ambiguous and is actually
specified by the choice of commuting cut-and-join morphisms, acting along the
edges of the hypercube -- this promotes it to Abelian quiver, and KR polynomial
is a Poincare polynomial of associated complex, just in the original Khovanov's
construction at N=2. This second step is still somewhat sophisticated -- though
incomparably simpler than its conventional matrix-factorization counterpart. In
this paper we concentrate on the first step, and provide just a mnemonic
treatment of the second step. Still, this is enough to demonstrate that all the
currently known examples of KR polynomials in the fundamental representation
can be easily reproduced in this new approach. As additional bonus we get a
simple description of the DGR relation between KR polynomials and
superpolynomials and demonstrate that the difference between reduced and
unreduced cases, which looks essential at KR level, practically disappears
after transition to superpolynomials. However, a careful derivation of all
these results from cohomologies of cut-and-join morphisms remains for further
studies. | Quantum, higher-spin, local charges in symmetric space sigma models: Potential anomalies are analysed for the local spin-3 and spin-4 classically
conserved currents in any two-dimensional sigma model on a compact symmetric
space $G/H$, with $G$ and $H$ classical groups. Quantum local conserved charges
are shown to exist in exactly those models which also possess quantum non-local
(Yangian) charges. The possibility of larger sets of quantum local charges is
discussed and shown to be consistent with known S-matrix results and the
behaviour of the corresponding Yangian representations. |
Hidden Symmetries of Euclideanised Kerr-NUT-(A)dS Metrics in Certain
Scaling Limits: The hidden symmetries of higher dimensional Kerr-NUT-(A)dS metrics are
investigated. In certain scaling limits these metrics are related to the
Einstein-Sasaki ones. The complete set of Killing-Yano tensors of the
Einstein-Sasaki spaces are presented. For this purpose the Killing forms of the
Calabi-Yau cone over the Einstein-Sasaki manifold are constructed. Two new
Killing forms on Einstein-Sasaki manifolds are identified associated with the
complex volume form of the cone manifolds. Finally the Killing forms on mixed
3-Sasaki manifolds are briefly described. | The SAGEX Review on Scattering Amplitudes, Chapter 6: Ambitwistor
Strings and Amplitudes from the Worldsheet: Starting with Witten's twistor string, chiral string theories have emerged
that describe field theory amplitudes without the towers of massive states of
conventional strings. These models are known as ambitwistor strings due to
their target space; the space of complexified null geodesics, also called
ambitwistor space. Correlators in these string theories directly yield compact
formulae for tree-level amplitudes and loop integrands, in the form of
worldsheet integrals fully localized on solutions to constraints known as the
scattering equations. In this chapter, we discuss two incarnations of the
ambitwistor string: a 'vector representation' starting in space-time and
structurally resembling the RNS superstring, and a four-dimensional twistorial
version closely related to, but distinct from Witten's original model. The
RNS-like models exist for several theories, with 'heterotic' and type II models
describing super-Yang-Mills and 10d supergravities respectively, and they
manifest the double copy relations directly at the level of the worldsheet
models. In the second half of the chapter, we explain how the underlying models
lead to diverse applications, ranging from extensions to new sectors of
theories, loop amplitudes and to scattering on curved backgrounds. We conclude
with a brief discussion of connections to conventional strings and celestial
holography. |
On three dimensional bigravity: In this paper we explore some features of f-g theory in three dimensions. We
show that the theory has (A)dS and (A)dS wave solutions. In particular at a
critical value of the coupling constant we see that the model admits Log
gravity solution as well, reminiscing TMG and NMG. We have also studied a class
of exact static spherically symmetric black hole solution in the model. | Infinite dimensional Lie algebras in 4D conformal quantum field theory: The concept of global conformal invariance (GCI) opens the way of applying
algebraic techniques, developed in the context of 2-dimensional chiral
conformal field theory, to a higher (even) dimensional space-time. In
particular, a system of GCI scalar fields of conformal dimension two gives rise
to a Lie algebra of harmonic bilocal fields, V_m(x,y), where the m span a
finite dimensional real matrix algebra M closed under transposition. The
associative algebra M is irreducible iff its commutant M' coincides with one of
the three real division rings. The Lie algebra of (the modes of) the bilocal
fields is in each case an infinite dimensional Lie algebra: a central extension
of sp(infty,R) corresponding to the field R of reals, of u(infty,infty)
associated to the field C of complex numbers, and of so*(4 infty) related to
the algebra H of quaternions. They give rise to quantum field theory models
with superselection sectors governed by the (global) gauge groups O(N), U(N),
and U(N,H)=Sp(2N), respectively. |
The Braided Heisenberg Group: We compute the braided groups and braided matrices $B(R)$ for the solution
$R$ of the Yang-Baxter equation associated to the quantum Heisenberg group. We
also show that a particular extension of the quantum Heisenberg group is dual
to the Heisenberg universal enveloping algebra $U_{q}(h)$, and use this result
to derive an action of $U_{q}(h)$ on the braided groups. We then demonstrate
the various covariance properties using the braided Heisenberg group as an
explicit example. In addition, the braided Heisenberg group is found to be
self-dual. Finally, we discuss a physical application to a system of n braided
harmonic oscillators. An isomorphism is found between the n-fold braided and
unbraided tensor products, and the usual `free' time evolution is shown to be
equivalent to an action of a primitive generator of $U_{q}(h)$ on the braided
tensor product. | D-branes and the Noncommutative Torus: We show that in certain superstring compactifications, gauge theories on
noncommutative tori will naturally appear as D-brane world-volume theories.
This gives strong evidence that they are well-defined quantum theories. It also
gives a physical derivation of the identification proposed by Connes, Douglas
and Schwarz of Matrix theory compactification on the noncommutative torus with
M theory compactification with constant background three-form tensor field. |
The Self-Dual Critical N=2 String: I review the covariant quantization of the closed fermionic string with (2,2)
extended world-sheet supersymmetry on R^{2,2}. Results on n-point scattering
amplitudes are presented, for tree- and one-loop world-sheets with arbitrary
Maxwell instanton number. I elaborate the connection between Maxwell moduli,
spectral flow, and instantons. It is argued that the latter serve to extend the
Lorentz symmetry from U(1,1) to SO(2,2) by undoing the choice of spacetime
complex structure. | Duality between Wilson loops and gluon amplitudes: An intriguing new duality between planar MHV gluon amplitudes and light-like
Wilson loops in N=4 super Yang-Mills is investigated. We extend previous checks
of the duality by performing a two-loop calculation of the rectangular and
pentagonal Wilson loop. Furthermore, we derive an all-order broken conformal
Ward identity for the Wilson loops and analyse its consequences. Starting from
six points, the Ward identity allows for an arbitrary function of conformal
invariants to appear in the expression for the Wilson loop. We compute this
function at six points and two loops and discuss its implications for the
corresponding gluon amplitude. It is found that the duality disagrees with a
conjecture for the gluon amplitudes by Bern et al. A recent calculation by Bern
et al indeed shows that the latter conjecture breaks down at six gluons and at
two loops. By doing a numerical comparison with their results we find that the
duality between gluon amplitudes and Wilson loops is preserved. This review is
based on the author's PhD thesis and includes developments until May 2008. |
$κ$--Rindler space: In this paper we construct, and investigate some thermal properties of, the
non-commutative counterpart of Rindler space, which we call $\kappa$--Rindler
space. This space is obtained by changing variables in the defining commutators
of $\kappa$--Minkowski space. We then re-derive the commutator structure of
$\kappa$--Rindler space with the help of an appropriate star product, obtained
from the $\kappa$--Minkowski one. Using this star product, following the idea
of Padmanabhan, we find the leading order, $1/\kappa$ correction to the Hawking
thermal spectrum. | Wilson-Fisher fixed points for any dimension: The critical behavior of a non-local scalar field theory is studied. This
theory has a non-local quartic interaction term which involves a real power
-\beta of the Laplacian. The parameter \beta can be tuned so as to make that
interaction marginal for any dimension. The lowest order Feynman diagrams
corresponding to coupling constant renormalization, mass renormalization, and
field renormalization are computed. In all cases a non-trivial IR fixed point
is obtained. Remarkably, for dimensions different from 4, field renormalization
is required at the one-loop level. For d=4, the theory reduces to the usual
local \phi^{4} field theory and field renormalization is required starting at
the the two-loop level. The critical exponents \nu and \eta are computed for
dimensions 2,3,4 and 5. For dimensions greater than four, the critical exponent
\eta turns out to be negative for \epsilon>0, which indicates a violation of
the unitarity bounds. |
A toy model for time evolving QFT on a lattice with controllable chaos: A class of models with a dynamics of generalized quantum cat maps on a
product of quantum tori is described. These tori are defined by an algebra of
clock-shift matrices of dimension $N$. The dynamics is such that the Lyapunov
exponents can be computed analytically at large $N$. Some of these systems can
be thought of as a toy model for quantum fields on a lattice under a time
evolution with nearest neighbor interactions, resembling a quantum version of a
cellular automaton. The dynamics of entangling is studied for initial product
states. Some of these entangle at rates determined by Lyapunov exponents of the
system at large $N$ when the initial states are gaussian. For other classes of
states, entanglement between two regions can be computed analytically: it is
found that entanglement rates are controlled by $\log(N)$. Some of these setups
can be realized on quantum computers with CNOT quantum gates. This is analyzed
in detail where we find that the dynamics has a self-similar behavior and
various peculiar behaviors. This dynamics can be interpreted in a particular
basis as a machine that broadcasts classical messages in one direction and that
produces over time a generalized GHZ state with the receiving region once we
consider superpositions of such messages. With the appropriate choice of
quantum vacuum on the receiving end of the system one can stop the message from
leaving the broadcast area. | Angles, scales and parametric renormalization: We decompose renormalized Feynman rules according to the scale and angle
dependence of amplitudes. We use parametric representations such that the
resulting amplitudes can be studied in algebraic geometry. |
Non-Thermal Phase Transitions after Inflation: At the first stage of reheating after inflation, parametric resonance may
rapidly transfer most of the energy of an inflaton field $\phi$ to the energy
of other bosons. We show that quantum fluctuations of scalar and vector fields
produced at this stage are much greater than they would be in a state of
thermal equilibrium. This leads to cosmological phase transitions of a new
type, which may result in a copious production of topological defects and in a
secondary stage of inflation after reheating. | The geometry of optimal functionals: In this paper, we give a geometric interpretation of optimal functionals in
the context of intersection of symmetry planes and cyclic polytopes. For 1D
CFTs, we demonstrate that at given derivative order, the functional is given by
a degenerate simplex of the cyclic polytope. More precisely the derivative
functionals at $2N{+}1$-th order, is given by an unique $N$-dimensional simplex
enclosing the origin. Taking the continuous limit, in the large $\Delta$
approximation this qualitatively agrees with that derived by Mazac et al.
Remarkably similar construction applies to 2D CFT in the diagonal limit as well
as the spin-less modular bootstrap. Finally we show that such geometric
interpretation can be extended to functionals associated with bounds beyond the
leading operator. |
Area Spectrum of Near Extremal Black Branes from Quasi-normal Modes: Motivated by the recent interest in quantization of black hole area spectrum,
we consider the area spectrum of near extremal black $3-$branes. Based on the
proposal by Bekenstein and others that the black hole area spectrum is discrete
and equally spaced, we implement Kunstatter's method to derive the area
spectrum for the near extremal black $3-$branes. The result for the area of
event horizon although discrete, is not equally spaced. | Multiverse Understanding of Cosmological Coincidences: There is a deep cosmological mystery: although dependent on very different
underlying physics, the timescales of structure formation, of galaxy cooling
(both radiatively and against the CMB), and of vacuum domination do not differ
by many orders of magnitude, but are all comparable to the present age of the
universe. By scanning four landscape parameters simultaneously, we show that
this quadruple coincidence is resolved. We assume only that the statistical
distribution of parameter values in the multiverse grows towards certain
catastrophic boundaries we identify, across which there are drastic regime
changes. We find order-of-magnitude predictions for the cosmological constant,
the primordial density contrast, the temperature at matter-radiation equality,
the typical galaxy mass, and the age of the universe, in terms of the fine
structure constant and the electron, proton and Planck masses. Our approach
permits a systematic evaluation of measure proposals; with the causal patch
measure, we find no runaway of the primordial density contrast and the
cosmological constant to large values. |
The Coulomb Branch of Yang-Mills Theory from the Schroedinger
Representation: The Coulomb branch of the potential between two static colored sources is
calculated for the Yang-Mills theory using the electric Schroedinger
representation. | Dyson-Schwinger equation approach to Lorentz Symmetry Breaking with
finite temperature and chemical potential: In this work, we investigate the dynamical breakdown of Lorentz symmetry in 4
dimensions by the condensation of a fermionic field described by a Dirac
Lagrangian with a four-fermion interaction. Using the Keldysh formalism we show
that the Lorentz symmetry breaking modifies the Dyson-Schwinger equations of
the fermionic propagator. We analyze the nonperturbative solutions for the
Dyson-Schwinger equations using the combination of the rainbow and quenched
approximations and show that, in equilibrium, the Lorentz symmetry breakdown
can occur in the strong coupling regime and new features arise from this
approach. Finally, we analyze the contributions of temperature and chemical
potential and find the respective phase diagram of the model and analyze the
dependence of the critical temperature and chemical potential as functions of
the coupling constant. |
Octonions and M-theory: We explain how structures related to octonions are ubiquitous in M-theory.
All the exceptional Lie groups, and the projective Cayley line and plane appear
in M-theory. Exceptional G_2-holonomy manifolds show up as compactifying
spaces, and are related to the M2 Brane and 3-form. We review this evidence,
which comes from the initial 11-dim structures. Relations between these objects
are stressed, when extant and understood. We argue for the necessity of a
better understanding of the role of the octonions themselves (in particular
non-associativity) in M-theory. | ADE functional dilogarithm identities and integrable models: We describe a new infinite family of multi-parameter functional equations for
the Rogers dilogarithm, generalizing Abel's and Euler's formulas. They are
suggested by the Thermodynamic Bethe Ansatz approach to the Renormalization
Group flow of 2D integrable, ADE-related quantum field theories. The known sum
rules for the central charge of critical fixed points can be obtained as
special cases of these. We conjecture that similar functional identities can be
constructed for any rational integrable quantum field theory with factorized
S-matrix and support it with extensive numerical checks. |
HHL correlators, orbit averaging and form factors: We argue that the conventional method to calculate the OPE coefficients in
the strong coupling limit for heavy-heavy-light operators in the N=4
Super-Yang-Mills theory has to be modified by integrating the light vertex
operator not only over a single string worldsheet but also over the moduli
space of classical solutions corresponding to the heavy states. This reflects
the fact that we are primarily interested in energy eigenstates and not
coherent states. We tested our prescription for the BMN vacuum correlator, for
folded strings on $S^5$ and for two-particle states. Our prescription for
two-particle states with the dilaton leads to a volume dependence which matches
exactly to the structure of finite volume diagonal formfactors. As the volume
depence does not rely on the particular light operator we conjecture that
symmetric OPE coefficients can be described for any coupling by finite volume
diagonal form factors. | Skyrmions and clustering in light nuclei: One of the outstanding problems in modern nuclear physics is to determine the
properties of nuclei from the fundamental theory of the strong force, quantum
chromodynamics (QCD). Skyrmions offer a novel approach to this problem by
considering nuclei as solitons of a low energy effective field theory obtained
from QCD. Unfortunately, the standard theory of Skyrmions has been plagued by
two significant problems, in that it yields nuclear binding energies that are
an order of magnitude larger than experimental nuclear data, and it predicts
intrinsic shapes for nuclei that fail to match the clustering structure of
light nuclei. Here we show that extending the standard theory of Skyrmions, by
including the next lightest subatomic meson particles traditionally neglected,
dramatically improves both these aspects. We find Skyrmion clustering that now
agrees with the expected structure of light nuclei, with binding energies that
are much closer to nuclear data. |
Perturbation theory in the Hamiltonian approach to Yang-Mills theory in
Coulomb gauge: We study the Hamiltonian approach to Yang-Mills theory in Coulomb gauge in
Rayleigh-Schroedinger perturbation theory. The static gluon and ghost
propagator as well as the potential between static colour sources are
calculated to one-loop order. Furthermore, the one-loop $\beta$-function is
calculated from both the ghost-gluon vertex and the static potential and found
to agree with the result of covariant perturbation theory. | On holographic time-like entanglement entropy: In order to study the pseudo entropy of time-like subregions holographically,
the previous smooth space-like extremal surface was recently generalized to mix
space-like and time-like segments and the area becomes complex value. This
paper finds that, if one tries to use such kind of piecewise smooth extremal
surfaces to compute time-like entanglement entropy holographically, the complex
area is not unique in general. We then generalize the original holographic
proposal of space-like entanglement entropy to pick up a unique area from all
allowed ``space-like+time-like'' piecewise smooth extremal surfaces for a
time-like subregion. We will give some concrete examples to show the
correctness of our proposal. |
Explicit BCJ numerators of nonlinear sigma model: In this paper, we investigate the color-kinematics duality in nonlinear sigma
model (NLSM). We present explicit polynomial expressions for the kinematic
numerators (BCJ numerators). The calculation is done separately in two
parametrization schemes of the theory using Kawai-Lewellen-Tye relation
inspired technique, both lead to polynomial numerators. We summarize the
calculation in each case into a set of rules that generates BCJ numerators for
all multilplicities. In Cayley parametrization we find the numerator is
described by a particularly simple formula solely in terms of momentum kernel. | Renormalization Group Flows on Line Defects: We consider line defects in d-dimensional Conformal Field Theories (CFTs).
The ambient CFT places nontrivial constraints on Renormalization Group (RG)
flows on such line defects. We show that the flow on line defects is
consequently irreversible and furthermore a canonical decreasing entropy
function exists. This construction generalizes the g theorem to line defects in
arbitrary dimensions. We demonstrate our results in a flow between Wilson loops
in 4 dimensions. |
Gravitational anomalies of fermionic higher-spin fields: Using the Atiyah-Singer index theorem, we formally compute gravitational
anomalies for fermionic higher-spin fields in two, six and ten dimensions, as
well as the U(1) mixed gauge-gravitational anomaly in four dimensions. In all
cases, anomaly cancellations are found for an infinite tower of fields with
alternating chiralities. | Black holes and membranes in AdS_7: We investigate maximal gauged supergravity in seven dimensions and some of
its solitonic solutions. By focusing on a truncation of the gauged SO(5)
R-symmetry group to its U(1)^2 Cartan subgroup, we construct general two charge
black holes that are asymptotically anti-de Sitter. We demonstrate that 1- and
2-charge black holes preserve 1/2 and 1/4 of the supersymmetries respectively.
Additionally, we examine the odd-dimensional self-duality equation governing
the three-form potential transforming as the 5 of SO(5), and provide some
insight on the construction of membrane solutions in anti-de Sitter
backgrounds. |
Extended BRS symmetry in topological field theories: A class of topological field theories like the $BF$ model and Chern-Simons
theory, when quantized in the Landau gauge, enjoys the property of invariance
under a vector supersymmetry, which is responsible for their finiteness. We
introduce a new type of gauge fixing which makes these theories invariant under
an extended $BRS$ symmetry, containing a new type of field, the ghost of
diffeomorphisms. The presence of such an extension is naturally related to the
vector supersymmetry discussed before. | Resolving anti-brane singularities through time-dependence: In this note we discuss a possible resolution of the flux singularities
associated with the insertion of branes in backgrounds supported by fluxes that
carry charges opposite to the branes. We present qualitative arguments that
such a setup could be unstable both in the closed and open string sector. The
singularities in the fluxes then get naturally resolved by taking the true
solution to be a time-dependent process in which flux gets attracted towards
the brane and subsequently annihilates. |
de Sitter Supersymmetry Revisited: We present the basic $\mathcal{N} =1$ superconformal field theories in
four-dimensional de Sitter space-time, namely the non-abelian super Yang-Mills
theory and the chiral multiplet theory with gauge interactions or cubic
superpotential. These theories have eight supercharges and are invariant under
the full $SO(4,2)$ group of conformal symmetries, which includes the de Sitter
isometry group $SO(4,1)$ as a subgroup. The theories are ghost-free and the
anti-commutator $\sum_\alpha\{Q_\alpha, Q^{\alpha\dagger}\}$ is positive. SUSY
Ward identities uniquely select the Bunch-Davies vacuum state. This vacuum
state is invariant under superconformal transformations, despite the fact that
de Sitter space has non-zero Hawking temperature. The $\mathcal{N}=1$ theories
are classically invariant under the $SU(2,2|1)$ superconformal group, but this
symmetry is broken by radiative corrections. However, no such difficulty is
expected in the $\mathcal{N}=4$ theory, which is presented in appendix B. | Cosmic vorticity on the brane: We study vector perturbations about four-dimensional brane-world cosmologies
embedded in a five-dimensional vacuum bulk. Even in the absence of matter
perturbations, vector perturbations in the bulk metric can support vector
metric perturbations on the brane. We show that during de Sitter inflation on
the brane vector perturbations in the bulk obey the same wave equation for a
massless five-dimensional field as found for tensor perturbations. However, we
present the second-order effective action for vector perturbations and find no
normalisable zero-mode in the absence of matter sources. The spectrum of
normalisable states is a continuum of massive modes that remain in the vacuum
state during inflation. |
Cosmelkology: Elko fermions in FLRW space-time: Cosmelkology is the study of Elko in cosmology. Elko is a massive spin-half
field of mass dimension one. Elko differs from the Dirac and Majorana fermions
because it furnishes the irreducible representation of the extended Poincare
group with a two-fold Wigner degeneracy where the particle and anti-particle
states both have four degrees of freedom. Elko has a renormalizable quartic
self interaction which makes it a candidate for self-interacting dark matter.
We study Elko in the spatially flat FLRW space-time and find exact solutions in
the de Sitter space. By choosing the appropriate solutions and phases, the
fields satisfy the canonical anti-commutation relations and have the correct
time evolutions in the flat space limit. | Small Cosmological Constants from a Modified Randall-Sundrum Model: We study a mechanism, inspired from the mechanism for generating the gauge
hierarchy in Randall-Sundrum model, to investigate the cosmological constant
problem. First we analyze the bulk cosmological constant and brane vacuum
energies in RS model. We show that the five-dimensional bulk cosmological
constant and the vacuum energies of the two branes all obtain their natural
values. Finally we argue how we can generate a small four-dimensional effective
cosmological constant on the branes through modifying the original RS model. |
The O(N) Monolith reloaded: Sum rules and Form Factor Bootstrap: We revisit the space of gapped quantum field theories with a global O(N)
symmetry in two spacetime dimensions. Previous works using S-matrix bootstrap
revealed a rich space in which integrable theories such as the non-linear sigma
model appear at special points on the boundary, along with an abundance of
unknown models hinting at a non conventional UV behaviour. We extend the
S-matrix set-up by including into the bootstrap form factors and spectral
functions for the stress-energy tensor and conserved O(N) currents. Sum rules
allow us to put bounds on the central charges of the conformal field theory
(CFT) in the UV. We find that a big portion of the boundary can only flow from
CFTs with infinite central charges. We track this result down to a particular
behaviour of the amplitudes in physical kinematics and discuss its physical
implications. | The Anatomy of Gauge/String Duality in Lunin-Maldacena Background: We consider the correspondence between the spinning string solutions in
Lunin-Maldacena background and the single trace operators in the
Leigh-Strassler deformation of N=4 SYM. By imposing an appropriate rotating
string ans\"atz on the Landau-Lifshitz reduced sigma model in the deformed
SU(2) sector, we find two types of `elliptic' solutions with two spins, which
turn out to be the solutions associated with the Neumann-Rosochatius system. We
then calculate the string energies as functions of spins, and obtain their
explicit forms in terms of a set of moduli parameters. On the deformed
spin-chain side, we explicitly compute the one-loop anomalous dimensions of the
gauge theory operators dual to each of the two types of spinning string
solutions, extending and complementing the results of hep-th/0511164. Moreover,
we propose explicit ans\"atze on how the locations of the Bethe strings are
affected due to the deformation, with several supports from the string side. |
Anharmonic oscillators, the thermodynamic Bethe ansatz, and nonlinear
integral equations: The spectral determinant $D(E)$ of the quartic oscillator is known to satisfy
a functional equation. This is mapped onto the $A_3$-related $Y$-system
emerging in the treatment of a certain perturbed conformal field theory,
allowing us to give an alternative integral expression for $D(E)$. Generalising
this result, we conjecture a relationship between the $x^{2M}$ anharmonic
oscillators and the $A_{2M-1}$ TBA systems. Finally, spectral determinants for
general $|x|^{\alpha}$ potentials are mapped onto the solutions of nonlinear
integral equations associated with the (twisted) XXZ and sine-Gordon models. | On the Classification of Brane Tilings: We present a computationally efficient algorithm that can be used to generate
all possible brane tilings. Brane tilings represent the largest class of
superconformal theories with known AdS duals in 3+1 and also 2+1 dimensions and
have proved useful for describing the physics of both D3 branes and also M2
branes probing Calabi-Yau singularities. This algorithm has been implemented
and is used to generate all possible brane tilings with at most 6
superpotential terms, including consistent and inconsistent brane tilings. The
collection of inconsistent tilings found in this work form the most
comprehensive study of such objects to date. |
Gauge Theories on ALE Space and Super Liouville Correlation Functions: We present a relation between N=2 quiver gauge theories on the ALE space
O_{P^1}(-2) and correlators of N=1 super Liouville conformal field theory,
providing checks in the case of punctured spheres and tori. We derive a blow-up
formula for the full Nekrasov partition function and show that, up to a U(1)
factor, the N=2^* instanton partition function is given by the product of the
character of \hat{SU}(2)_2 times the super Virasoro conformal block on the
torus with one puncture. Moreover, we match the perturbative gauge theory
contribution with super Liouville three-point functions. | Remarks on the M5-Brane: The fivebrane of M theory -- the M5-brane -- is an especially interesting
object. It plays a central role in a geometric understanding of the
Seiberg-Witten solution of N=2 D=4 gauge theories as well as in certain new 6d
quantum theories. The low energy effective action is an interacting theory of a
(2,0) tensor multiplet. The fact that this multiplet contains a two-form gauge
field with a self-dual field strength poses special challenges. Recent progress
in addressing those challenges is reviewed. |
Extravariables in the BRST Quantization of Second-Class Constrained
Systems; Existence Theorems: In this paper we show how the BRST quantization can be applied to systems
possessing only second-class constraints through their conversion to some
first-class ones starting with our method exposed in [Nucl.Phys. B456
(1995)473]. Thus, it is proved that i) for a certain class of second-class
systems there exists a standard coupling between the variables of the original
phase-space and some extravariables such that we can transform the original
system into a one-parameter family of first-class systems; ii) the BRST
quantization of this family in a standard gauge leads to the same path integral
as that of the original system. The analysis is accomplished in both reducible
and irreducible cases. In the same time, there is obtained the Lagrangian
action of the first-class family and its provenience is clarified. In this
context, the Wess-Zumino action is also derived. The results from the
theoretical part of the paper are exemplified in detail for the massive
Yang-Mills theory and for the massive abelian three-form gauge fields. | Higgs and Coulomb Branch Descriptions of the Volume of the Vortex Moduli
Space: BPS vortex systems on closed Riemann surfaces with arbitrary genus are
embedded into two-dimensional supersymmetric Yang-Mills theory with matters. We
turn on a background R-gauge fields to keep half of rigid supersymmetry
(topological A-twist) on the curved space. We consider two complementary
descriptions; Higgs and Coulomb branches. The path integral reduces to the zero
mode integral by the localization in the Higgs branch. The integral over the
bosonic zero modes directly gives an integral over the volume form of the
moduli space, whereas the fermionic zero modes are compensated by an
appropriate operator insertion. In the Coulomb branch description with the same
operator insertion, the path integral reduces to a finite-dimensional residue
integral. The operator insertion automatically determines a choice of integral
contours, leading to the Jeffrey-Kirwan residue formula. This result ensures
the existence of the solution to the BPS vortex equation and explains the
Bradlow bounds of the BPS vortex. We also discuss a generating function of the
volume of the vortex moduli space and show a reduction of the moduli space from
semi-local to local vortices. |
Scalar and Spinor Two-Point Functions in Einstein Universe: Two-point functions for scalar and spinor fields are investigated in Einstein
universe ($R \otimes S^{\sN-1}$). Equations for massive scalar and spinor
two-point functions are solved and the explicit expressions for the two-point
functions are given. The simpler expressions for massless cases are obtained
both for the scalar and spinor cases. | Divergences of Discrete States Amplitudes and Effective Lagrangian in 2D
String Theory: Scattering amplitudes for discrete states in 2D string theory are considered.
Pole divergences of tree-level amplitudes are extracted and residues are
interpreted as renormalized amplitudes for discrete states. An effective
Lagrangian generating renormalized amplitudes for open string is written and
corresponding Ward identities are presented. A relation of this Lagrangian with
homotopy Lie algebra is discussed. |
Multi-particle States from the Effective Action for Local Composite
Operators: Anharmonic Oscillator: The effective action for the local composite operator $\Phi^2(x)$ in the
scalar quantum field theory with $\lambda\Phi^4$ interaction is obtained in the
expansion in two-particle-point-irreducible (2PPI) diagrams up to five-loops.
The effective potential and 2-point Green's functions for elementary and
composite fields are derived. The ground state energy as well as one- and
two-particle excitations are calculated for space-time dimension $n=1$, when
the theory is equivalent to the quantum mechanics of an anharmonic oscillator.
The agreement with the exact spectrum of the oscillator is much better than
that obtained within the perturbation theory. | Asymptotic safety guaranteed: We study the ultraviolet behaviour of four-dimensional quantum field theories
involving non-abelian gauge fields, fermions and scalars in the Veneziano
limit. In a regime where asymptotic freedom is lost, we explain how the three
types of fields cooperate to develop fully interacting ultraviolet fixed
points, strictly controlled by perturbation theory. Extensions towards strong
coupling and beyond the large-N limit are discussed. |
Non Abelian Vortices as Instantons on Noncommutative Discrete Space: There seems to be close relationship between the moduli space of vortices and
the moduli space of instantons, which is not yet clearly understood from a
standpoint of the field theory. We clarify the reasons why many similarities
are found in the methods for constructing the moduli of instanton and vortex,
viewed in the light of the notion of the self-duality. We show that the
non-Abelian vortex is nothing but the instanton in $R^{2} \times Z_{2}$ from a
viewpoint of the noncommutative differential geometry and the gauge theory in
discrete space. The action for pure Yang-Mills theory in $R^{2} \times Z_{2}$
is equivalent to that for Yang-Mills-Higgs theory in $R^{2} $. | Interactions of Massless Higher Spin Fields From String Theory: We construct vertex operators for massless higher spin fields in RNS
superstring theory and compute some of their three-point correlators,
describing gauge-invariant cubic interactions of the massless higher spins. The
Fierz-Pauli on-shell conditions for the higher spins (including tracelessness
and vanishing divergence) follow from the BRST-invariance conditions for the
vertex operators constructed in this paper. The gauge symmetries of the
massless higher spins emerge as a result of the BRST nontriviality conditions
for these operators, being equivalent to transformations with the traceless
gauge parameter in the Fronsdal's approach. The gauge invariance of the
interaction terms of the higher spins is therefore ensured automatically by
that of the vertex operators in string theory. We develop general algorithm to
compute the cubic interactions of the massless higher spins and use it to
explicitly describe the gauge-invariant interaction of two $s=3$ and one $s=4$
massless particles. |
Asymptotic safety guaranteed in supersymmetry: We explain how asymptotic safety arises in four-dimensional supersymmetric
gauge theories. We provide asymptotically safe supersymmetric gauge theories
together with their superconformal fixed points, R-charges, phase diagrams, and
UV-IR connecting trajectories. Strict perturbative control is achieved in a
Veneziano limit. Consistency with unitarity and the a-theorem is established.
We find that supersymmetry enhances the predictivity of asymptotically safe
theories. | Gravitational duals to the grand canonical ensemble abhor Cauchy
horizons: The gravitational dual to the grand canonical ensemble of a large $N$
holographic theory is a charged black hole. These spacetimes -- for example
Reissner-Nordstr\"om-AdS -- can have Cauchy horizons that render the classical
gravitational dynamics of the black hole interior incomplete. We show that a
(spatially uniform) deformation of the CFT by a neutral scalar operator
generically leads to a black hole with no inner horizon. There is instead a
spacelike Kasner singularity in the interior. For relevant deformations, Cauchy
horizons never form. For certain irrelevant deformations, Cauchy horizons can
exist at one specific temperature. We show that the scalar field triggers a
rapid collapse of the Einstein-Rosen bridge at the would-be Cauchy horizon.
Finally, we make some observations on the interior of charged dilatonic black
holes where the Kasner exponent at the singularity exhibits an attractor
mechanism in the low temperature limit. |
Fractional Supersymmetry through Generalized Anyonic algebra: The construction of anyonic operators and algebra is generalized by using
quons operators. Therefore, the particular versionof fractional supersymmetry
is constructed on the two-dimensional lattice by associating two generalized
anyons of different kinds. The fractional supersymmetry Hamiltonian operator is
obtained on the two-dimensional lattice and the quantum algebra $U_{q}(sl_{2})$
is realized. | Sequestering in String Compactifications: We study the mediation of supersymmetry breaking in string compactifications
whose moduli are stabilized by nonperturbative effects. We begin with a
critical review of arguments for sequestering in supergravity and in string
theory. We then show that geometric isolation, even in a highly warped space,
is insufficient to achieve sequestering: in type IIB compactifications,
nonperturbative superpotentials involving the Kahler moduli introduce
cross-couplings between well-separated visible and hidden sectors. The scale of
the resulting soft terms depends on the moduli stabilization scenario. In the
Large Volume Scenario, nonperturbative superpotential contributions to the soft
trilinear $A$ terms can introduce significant flavor violation, while in KKLT
compactifications their effects are negligible. In both cases, the
contributions to the $\mu$ and $B\mu$ parameters cannot be ignored in general.
We conclude that sequestered supersymmetry breaking is possible in
nonperturbatively-stabilized compactifications only if a mechanism in addition
to bulk locality suppresses superpotential cross-couplings. |
No chiral truncation of quantum log gravity?: At the classical level, chiral gravity may be constructed as a consistent
truncation of a larger theory called log gravity by requiring that left-moving
charges vanish. In turn, log gravity is the limit of topologically massive
gravity (TMG) at a special value of the coupling (the chiral point). We study
the situation at the level of linearized quantum fields, focussing on a unitary
quantization. While the TMG Hilbert space is continuous at the chiral point,
the left-moving Virasoro generators become ill-defined and cannot be used to
define a chiral truncation. In a sense, the left-moving asymptotic symmetries
are spontaneously broken at the chiral point. In contrast, in a non-unitary
quantization of TMG, both the Hilbert space and charges are continuous at the
chiral point and define a unitary theory of chiral gravity at the linearized
level. | Lorentz-preserving fields in Lorentz-violating theories: We identify a fairly general class of field configurations (of spins 0, 1/2
and 1) which preserve Lorentz invariance in effective field theories of Lorentz
violation characterized by a constant timelike vector. These fields
concomitantly satisfy the equations of motion yielding cubic dispersion
relations similar to those found earlier. They appear to have prospective
applications in inflationary scenarios. |
A strongly coupled anyon material: We use alternative quantisation of the D3-D5 system to explore properties of
a strongly coupled anyon material at finite density and temperature. We study
the transport properties of the material and find both diffusion and massive
holographic zero sound modes. By studying the anyon number conductivity we also
find evidence for the anyonic analogue of the metal-insulator transition. | Towards New Classes of Flux Compactifications: We derive novel solutions of flux compactification with D7-branes on the
resolved conifold in type IIB String Theory and later extend this solution to
allow for non-zero temperature. At zero temperature, we find that adding
D7-branes via the Ouyang embedding contributes to the supersymmetry-breaking
(1,2) imaginary-self-dual flux, without generating a bulk cosmological
constant. We further find that having D7-branes and a resolved conifold
together give rise to a non-trivial D-term on the D7-branes. This
supersymmetry-breaking term vanishes when we take the singular conifold limit,
although supersymmetry appears to remain broken. We also lift our construction
to F-theory where we show that the type IIB (1,2) flux goes to (2,2)
non-primitive flux on the fourfold.
In the second part of the thesis, we extend these results by taking the
non-extremal limit of our geometry to incorporate temperature. In this case,
the internal NS-NS and R-R fluxes are no longer expected to be self-dual, but
they should also naturally be extensions of the fluxes found above. From the
supergravity equations of motion, we compute how the new contributions to the
fluxes should enter, due to the squashing of the resolved metric and
non-extremality. This provides us with a compelling gravity dual of large N
thermal quantum chromodynamics with flavor. |
M2-brane Flows and the Chern-Simons Level: The Chern-Simons level k of ABJM gauge theory captures the orbifolding in the
dual geometry. This suggests that if we move the membranes away from the tip of
the orbifold to a smooth point, it should trigger an RG flow that changes the
level to k=1 in the IR. We construct an explicit supergravity solution that is
dual to this shift from generic k to k=1. In the gauge theory side, we present
arguments for why this shift is plausible at the end of the RG flow. We also
consider a resolution of the orbifold for the case k=4 (where explicit metrics
can be found), and construct the smooth supergravity solution that interpolates
between AdS4 X S7/Z4 and AdS4 X S7, corresponding to localized branes on the
blown up six cycle. In the gauge theory, we make some comments about the
dimension four operator dual to the resolution as well as the associated RG
flow. | Caustic Formation in Tachyon Effective Field Theories: Certain configurations of D-branes, for example wrong dimensional branes or
the brane-antibrane system, are unstable to decay. This instability is
described by the appearance of a tachyonic mode in the spectrum of open strings
ending on the brane(s). The decay of these unstable systems is described by the
rolling of the tachyon field from the unstable maximum to the minimum of its
potential. We analytically study the dynamics of the inhomogeneous tachyon
field as it rolls towards the true vacuum of the theory in the context of
several different tachyon effective actions. We find that the vacuum dynamics
of these theories is remarkably similar and in particular we show that in all
cases the tachyon field forms caustics where second and higher derivatives of
the field blow up. The formation of caustics signals a pathology in the
evolution since each of the effective actions considered is not reliable in the
vicinity of a caustic. We speculate that the formation of caustics is an
artifact of truncating the tachyon action, which should contain all orders of
derivatives acting on the field, to a finite number of derivatives. Finally, we
consider inhomogeneous solutions in p-adic string theory, a toy model of the
bosonic tachyon which contains derivatives of all orders acting on the field.
For a large class of initial conditions we conclusively show that the evolution
is well behaved in this case. It is unclear if these caustics are a genuine
prediction of string theory or not. |
Heavy Fermion Stabilization of Solitons in 1+1 Dimensions: We find static solitons stabilized by quantum corrections in a
(1+1)-dimensional model with a scalar field chirally coupled to fermions. This
model does not support classical solitons. We compute the renormalized energy
functional including one-loop quantum corrections. We carry out a variational
search for a configuration that minimizes the energy functional. We find a
nontrivial configuration with fermion number whose energy is lower than the
same number of free fermions quantized about the translationally invariant
vacuum. In order to compute the quantum corrections for a given background
field we use a phase-shift parameterization of the Casimir energy. We identify
orders of the Born series for the phase shift with perturbative Feynman
diagrams in order to renormalize the Casimir energy using perturbatively
determined counterterms. Generalizing dimensional regularization, we
demonstrate that this procedure yields a finite and unambiguous energy
functional. | String creation in cosmologies with a varying dilaton: FRW solutions of the string theory low-energy effective actions are
described, yielding a dilaton which first decreases and then increases. We
study string creation in these backgrounds and find an exponential divergence
due to an initial space-like singularity. We conjecture that this singularity
may be removed by the effects of back-reaction, leading to a solution which at
early times is de Sitter space. |
An infinite square-well potential as a limiting case of a finite
square-well potential in a minimal-length scenario: One of the most widely problem studied in quantum mechanics is of an infinite
square-well potential. In a minimal-length scenario its study requires
additional care because the boundary conditions at the walls of the well are
not well fixed. In order to avoid this we solve the finite square-well
potential whose the boundary conditions are well fixed, even in a
minimal-length scenario, and then we take the limit of the potential going to
infinity to find the eigenfunctions and the energy equation for the infinite
square-well potential. Although the first correction for the energy eigenvalues
is the same one has been found in the literature, our result shows that the
eigenfunctions have the first derivative continuous at the square-well walls
what is in disagreement those previous work. That is because in the literature
the authors have neglected the hyperbolic solutions and have assumed the
discontinuity of the first derivative of the eigenfunctions at the walls of the
infinite square-well which is not correct. As we show, the continuity of the
first derivative of the eigenfunctions at the square-well walls guarantees the
continuity of the probability current density and the unitarity of the time
evolution | Functional Integral Approach to the N-Flavor Schwinger Model: We study massless QED_2 with N flavors using path integrals. We identify the
sector that is generated by the N^2 classically conserved vector currents. One
of them (the U(1) current) creates a massive particle, while the others create
massless ones. We show that the mass spectrum obeys a Witten-Veneziano type
formula. Two theorems on n-point functions clarify the structure of the Hilbert
space. Evaluation of the Fredenhagen-Marcu order parameter indicates that a
confining force exists only between charges that are integer multiples of +/-
Ne, whereas charges that are nonzero mod(N) screen their confining forces and
lead to non-vacuum sectors. Finally we identify operators that violate
clustering, and decompose the theory into clustering theta vacua. |
Manifestly gauge invariant computations: Using a gauge invariant exact renormalization group, we show how to compute
the effective action, and extract the physics, whilst manifestly preserving
gauge invariance at each and every step. As an example we give an elegant
computation of the one-loop SU(N) Yang-Mills beta function, for the first time
at finite N without any gauge fixing or ghosts. It is also completely
independent of the details put in by hand, e.g. the choice of covariantisation
and the cutoff profile, and, therefore, guides us to a procedure for
streamlined calculations. | QCD Dynamics From M-Theory: The field theories on the surface of non-supersymmetric D-brane constructions
are identified. By moving to M-theory a semi-classical, strong coupling
expansion to the IR non-supersymmetric gauge dynamics is obtained. The solution
is consistent with the formation of a quark condensate but there is evidence
that in moving to strong coupling scalar degrees of freedom have not decoupled. |
Hilbert Space Representation of an Algebra of Observables for q-Deformed
Relativistic Quantum Mechanics: Using a representation of the q-deformed Lorentz algebra as differential
operators on quantum Minkowski space, we define an algebra of observables for a
q-deformed relativistic quantum mechanics with spin zero. We construct a
Hilbert space representation of this algebra in which the square of the mass $
p^2 $ is diagonal. | A systematic approach to model building: We outline a new, systematic way of constructing and analysing field
theories, where all possible continuous symmetries of a given model are derived
using the method of Lie point symmetries. If the model has free parameters, and
relationships amongst any of these parameters yields an enhanced symmetry, then
all such relationships are found, along with the resulting symmetry group. We
discuss how the method can be applied to the standard model and beyond, to
direct the search for a more predictive field theory. The method handles
compact and non-compact continuous groups, spontaneously broken symmetries, and
is also applicable to general relativity. |
Voros product, noncommutative inspired Reissner-Nordstr{ö}m black hole
and corrected area law: We emphasize the importance of the Voros product in defining a noncommutative
inspired Reissner-Nordstr\"{o}m black hole. The entropy of this black hole is
then computed in the tunneling approach and is shown to obey the area law at
the next to leading order in the noncommutative parameter $\theta$.
Modifications to entropy/area law is then obtained by going beyond the
semi-classical approximation. The leading correction to the semiclassical
entropy/area law is found to be logarithmic and its coefficient involves the
noncommutative parameter $\theta$. | On q-deformed symmetries as Poisson-Lie symmetries and application to
Yang-Baxter type models: Yang-Baxter type models are integrable deformations of integrable field
theories, such as the principal chiral model on a Lie group $G$ or
$\sigma$-models on (semi-)symmetric spaces $G/F$. The deformation has the
effect of breaking the global $G$-symmetry of the original model, replacing the
associated set of conserved charges by ones whose Poisson brackets are those of
the $q$-deformed Poisson-Hopf algebra $\mathscr U_q(\mathfrak g)$. Working at
the Hamiltonian level, we show how this $q$-deformed Poisson algebra originates
from a Poisson-Lie $G$-symmetry. The theory of Poisson-Lie groups and their
actions on Poisson manifolds, in particular the formalism of the non-abelian
moment map, is reviewed. For a coboundary Poisson-Lie group $G$, this
non-abelian moment map must obey the Semenov-Tian-Shansky bracket on the dual
group $G^*$, up to terms involving central quantities. When the latter vanish,
we develop a general procedure linking this Poisson bracket to the defining
relations of the Poisson-Hopf algebra $\mathscr U_q(\mathfrak g)$, including
the $q$-Poisson-Serre relations. We consider reality conditions leading to $q$
being either real or a phase. We determine the non-abelian moment map for
Yang-Baxter type models. This enables to compute the corresponding action of
$G$ on the fields parametrising the phase space of these models. |
Ground states of a Klein-Gordon field with Robin boundary conditions in
global anti-de Sitter spacetime: We consider a real, massive scalar field both on the $n$-dimensional anti--de
Sitter (AdS$_n$) spacetime and on its universal cover CAdS$_n$. In the second
scenario, we extend the recent analysis on PAdS$_n$, the Poincar\'e patch of
AdS$_n$, first determining all admissible boundary conditions of Robin type
that can be applied on the conformal boundary. Most notably, contrary to what
happens on PAdS$_n$, no bound state mode solution occurs. Subsequently, we
address the problem of constructing the two-point function for the ground state
satisfying the admissible boundary conditions. All these states are locally of
Hadamard form being obtained via a mode expansion which encompasses only the
positive frequencies associated to the global timelike Killing field on
CAdS$_n$. To conclude we investigate under which conditions any of the
two-point correlation functions constructed on the universal cover defines a
counterpart on AdS$_n$, still of Hadamard form. Since this spacetime is
periodic in time, it turns out that this is possible only for Dirichlet
boundary conditions, though for a countable set of masses of the underlying
field, or for Neumann boundary conditions, though only for even dimensions and
for one given value of the mass. | Canonical Chern-Simons Theory and the Braid Group on a Riemann Surface: We examine the problem of determining which representations of the braid
group on a Riemann surface are carried by the wave function of a quantized
Abelian Chern-Simons theory interacting with non-dynamical matter. We
generalize the quantization of Chern-Simons theory to the case where the
coefficient of the Chern-Simons term, $k$, is rational, the Riemann surface has
arbitrary genus and the total matter charge is non-vanishing. We find an
explicit solution of the Schr\"odinger equation. We find that the wave
functions carry a representation of the braid group as well as a projective
representation of the discrete group of large gauge transformations. We find a
fundamental constraint which relates the charges of the particles, $q_i$, the
coefficient $k$ and the genus of the manifold, $g$. |
Effective Planck Mass and the Scale of Inflation: A recent paper argued that it is not possible to infer the energy scale of
inflation from the amplitude of tensor fluctuations in the Cosmic Microwave
Background, because the usual connection is substantially altered if there are
a large number of universally coupled fields present during inflation, with
mass less than the inflationary Hubble scale. We give a simple argument
demonstrating that this is incorrect. | Encoding the lattice in the Holography: One of the most wanted features of holography in its condensed matter physics
application is to encode the structure of lattice, which is the most direct
data of the material. In this paper, we propose a method to encode the lattice
structure by embedding the tight binding data into the Dirac equation in the
AdS bulk. We explicitly worked out the idea for the Graphene and Haldane model,
and the result shows that some degrees of freedom escape the free-electron
on-shell curve, and Green's function loses the pole structure completely. It
implies that the electronic structure is not described by the band structure
only, which is consistent with what many ARPES data tell us, and it also
implies that the system is in non-fermi liquid even for the graphene, which is
consistent with recent experiments for the clean graphene. |
Discrete Torsion, AdS/CFT and duality: We analyse D-branes on orbifolds with discrete torsion, extending earlier
results. We analyze certain Abelian orbifolds of the type C^3/ \Gamma, where
\Gamma is given by Z_m x Z_n, for the most general choice of discrete torsion
parameter. By comparing with the AdS/CFT correspondence, we can consider
different geometries which give rise to the same physics. This identifies new
mirror pairs and suggests new dualities at large N. As a by-product we also get
a more geometric picture of discrete torsion. | More about the $j=0$ relativistic oscillator: I start from the Bargmann-Wigner equations and introduce an interaction in
the form which is similar to a $j=1/2$ case [M. Moshinsky & A. Szczepaniak,
{\it J. Phys. A}{\bf 22} (1989) L817]. By means of the expansion of the wave
function in the complete set of $\gamma$- matrices one can obtain the equations
for a system which could be named as the $j=0$ Kemmer-Dirac oscillator.
The equations for the components $\phi_1$ and $\phi_2$ are different from the
ones obtained by Y. Nedjadi & R. Barrett for the $j=0$ Duffin-Kemmer-Petiau
oscillator [{\it J. Phys. A} {\bf 27} (1994) 4301]. This fact leads to the
dissimilar energy spectrum of the $j=0$ relativistic oscillator. |
The Octagon as a Determinant: The computation of a certain class of four-point functions of heavily charged
BPS operators boils down to the computation of a special form factor - the
octagon. In this paper, which is an extended version of the short note [1], we
derive a non-perturbative formula for the square of the octagon as the
determinant of a semi-infinite skew-symmetric matrix. We show that
perturbatively in the weak coupling limit the octagon is given by a determinant
constructed from the polylogarithms evaluating ladder Feynman graphs. We also
give a simple operator representation of the octagon in terms of a vacuum
expectation value of massless free bosons or fermions living in the rapidity
plane. | Two Dimensional Quantum Gravity Coupled to Matter: A classical two dimensional theory of gravity which has a number of
interesting features (including a Newtonian limit, black holes and
gravitational collapse) is quantized using conformal field theoretic
techniques. The critical dimension depends upon Newton's constant, permitting
models with $d=4$. The constraint algebra and scaling properties of the model
are computed. |
Newton-Cartan $ D 0$ branes from $ D1 $ branes and integrability: We explore analytic integrability criteria for $ D1 $ branes probing 4D
relativistic background with a null isometry direction. We use both the
Kovacic's algorithm of classical (non)integrability as well as the standard
formulation of Lax connections to show the analytic integrability of the
associated dynamical configuration. We further use the notion of double null
reduction and obtain the world-volume action corresponding to a torsional
Newton-Cartan (TNC) $ D0 $ brane probing a 3D torsional Newton-Cartan geometry.
Moreover, following Kovacic's method, we show the classical integrability of
the TNC $ D0 $ brane configuration thus obtained. Finally, considering a
trivial field redefinition for the $ D1 $ brane world-volume fields, we show
the equivalence between two configurations in the presence of vanishing NS
fluxes. | Low Energy Pion-Pion Elastic Scattering in Sakai-Sugimoto Model: We have considered the holographic large $N_c$ QCD model proposed by Sakai
and Sugimoto and evaluated the non-Abelian DBI-action on the D8-brane upto
$(\alpha')^4$ terms. Restricting to the pion sector, these corrections give
rise to four derivative contact terms for the pion field. We derive the
Weinberg's phenemenological lagrangian. The coefficients of the four derivative
terms are determined in terms of $g_{YM}^2$. The low energy pion-pion
scattering amplitudes are evaluated. Numerical results are presented with the
choice of $M_{KK}=0.94 GeV$ and $N_c=11$. The results are compared with the
amplitudes calculated using the experimental phase shifts. The agreement with
the experimental data is found to be satisfactory. |
CP Violation and Baryogenesis in the Presence of Black Holes: In a recent paper[1] Kundu and one of the present authors showed that there
were transient but observable CP violating effects in the decay of classical
currents on the horizon of a black hole, if the Lagrangian of the Maxwell field
contained a CP violating angle {\theta}. In this paper we demonstrate that a
similar effect can be seen in the quantum mechanics of QED: a non-trivial Berry
phase in the QED wave function is produced by in-falling electric charges. We
also investigate whether CP violation, of this or any other type, might be used
to produce the baryon asymmetry of the universe, in models where primordial
black hole decay contributes to the matter content of the present universe.
This can happen both in a variety of hybrid inflation models, and in the
Holographic Space-time (HST) model of inflation[2]. | Attractors with Vanishing Central Charge: We consider the Attractor Equations of particular $\mathcal{N}=2$, d=4
supergravity models whose vector multiplets' scalar manifold is endowed with
homogeneous symmetric cubic special K\"{a}hler geometry, namely of the
so-called $st^{2}$ and $stu$ models. In this framework, we derive explicit
expressions for the critical moduli corresponding to non-BPS attractors with
vanishing $\mathcal{N}=2$ central charge. Such formul\ae hold for a generic
black hole charge configuration, and they are obtained without formulating any
\textit{ad hoc} simplifying assumption. We find that such attractors are
related to the 1/2-BPS ones by complex conjugation of some moduli. By uplifting
to $\mathcal{N}=8$, d=4 supergravity, we give an interpretation of such a
relation as an exchange of two of the four eigenvalues of the $\mathcal{N}=8$
central charge matrix $Z_{AB}$. We also consider non-BPS attractors with
non-vanishing $\mathcal{Z}$; for peculiar charge configurations, we derive
solutions violating the Ansatz usually formulated in literature. Finally, by
group-theoretical considerations we relate Cayley's hyperdeterminant (the
invariant of the stu model) to the invariants of the st^{2} and of the
so-called t^{3} model. |
Parity-Violating Hydrodynamics in 2+1 Dimensions: We study relativistic hydrodynamics of normal fluids in two spatial
dimensions. When the microscopic theory breaks parity, extra transport
coefficients appear in the hydrodynamic regime, including the Hall viscosity,
and the anomalous Hall conductivity. In this work we classify all the transport
coefficients in first order hydrodynamics. We then use properties of response
functions and the positivity of entropy production to restrict the possible
coefficients in the constitutive relations. All the parity-breaking transport
coefficients are dissipationless, and some of them are related to the
thermodynamic response to an external magnetic field and to vorticity. In
addition, we give a holographic example of a strongly interacting relativistic
fluid where the parity-violating transport coefficients are computable. | Evaluating the Wald Entropy from two-derivative terms in quadratic
actions: We evaluate the Wald Noether charge entropy for a black hole in generalized
theories of gravity. Expanding the Lagrangian to second order in gravitational
perturbations, we show that contributions to the entropy density originate only
from the coefficients of two-derivative terms. The same considerations are
extended to include matter fields and to show that arbitrary powers of matter
fields and their symmetrized covariant derivatives cannot contribute to the
entropy density. We also explain how to use the linearized gravitational field
equation rather than quadratic actions to obtain the same results. Several
explicit examples are presented that allow us to clarify subtle points in the
derivation and application of our method. |
Composite black holes in external fields: The properties of composite black holes in the background of electric or
magnetic flux tubes are analyzed, both when the black holes remain in static
equilibrium and when they accelerate under a net external force. To this
effect, we present a number of exact solutions (generalizing the Melvin, C and
Ernst solutions) describing these configurations in a theory that admits
composite black holes with an arbitrary number of constituents. The
compositeness property is argued to be independent of supersymmetry. Even if,
in general, the shape of the horizon is distorted by the fields, the dependence
of the extreme black hole area on the charges is shown to remain unchanged by
either the external fields or the acceleration. We also discuss pair creation
of composite black holes. In particular, we extend a previous analysis of pair
creation of massless holes. Finally, we give the generalization of our
solutions to include non-extreme black holes. | Revisiting non-Gaussianity in non-attractor inflation models in the
light of the cosmological soft theorem: We revisit the squeezed-limit non-Gaussianity in the single-field
non-attractor inflation models from the viewpoint of the cosmological soft
theorem. In the single-field attractor models, inflaton's trajectories with
different initial conditions effectively converge into a single trajectory in
the phase space, and hence there is only one \emph{clock} degree of freedom
(DoF) in the scalar part. Its long-wavelength perturbations can be absorbed
into the local coordinate renormalization and lead to the so-called
\emph{consistency relation} between $n$- and $(n+1)$-point functions. On the
other hand, if the inflaton dynamics deviates from the attractor behavior, its
long-wavelength perturbations cannot necessarily be absorbed and the
consistency relation is expected not to hold any longer. In this work, we
derive a formula for the squeezed bispectrum including the explicit correction
to the consistency relation, as a proof of its violation in the non-attractor
cases. First one must recall that non-attractor inflation needs to be followed
by attractor inflation in a realistic case. Then, even if a specific
non-attractor phase is effectively governed by a single DoF of phase space
(represented by the exact ultra-slow-roll limit) and followed by a single-DoF
attractor phase, its transition phase necessarily involves two DoF in dynamics
and hence its long-wavelength perturbations cannot be absorbed into the local
coordinate renormalization. Thus, it can affect local physics, even taking
account of the so-called \emph{local observer effect}, as shown by the fact
that the bispectrum in the squeezed limit can go beyond the consistency
relation. More concretely, the observed squeezed bispectrum does not vanish in
general for long-wavelength perturbations exiting the horizon during a
non-attractor phase. |
Heterotic T-fects, 6D SCFTs, and F-Theory: We study the $(1,0)$ six-dimensional SCFTs living on defects of non-geometric
heterotic backgrounds (T-fects) preserving a $E_7\times E_8$ subgroup of
$E_8\times E_8$. These configurations can be dualized explicitly to F-theory on
elliptic K3-fibered non-compact Calabi-Yau threefolds. We find that the
majority of the resulting dual threefolds contain non-resolvable singularities.
In those cases in which we can resolve the singularities we explicitly
determine the SCFTs living on the defect. We find a form of duality in which
distinct defects are described by the same IR fixed point. For instance, we
find that a subclass of non-geometric defects are described by the SCFT arising
from small heterotic instantons on ADE singularities. | Holography on the Quantum Disk: Motivated by recent study of DSSYK and the non-commutative nature of its bulk
dual, we review and analyze an example of a non-commutative spacetime known as
the quantum disk proposed by L. Vaksman. The quantum disk is defined as the
space whose isometries are generated by the quantum algebra
$U_q(\mathfrak{su}_{1,1})$. We review how this algebra is defined and its
associated group $SU_q(1,1)$ that it generates, highlighting its non-trivial
coproduct that sources bulk non-commutativity. We analyze the structure of
holography on the quantum disk and study the imprint of non-commutativity on
the putative boundary dual. |
Proof of the Julia-Zee Theorem: It is a well accepted principle that finite-energy static solutions in the
classical relativistic gauge field theory over the $(2+1)$-dimensional
Minkowski spacetime must be electrically neutral. We call such a statement the
Julia--Zee theorem. In this paper, we present a mathematical proof of this
fundamental structural property. | Heterotic Little String Theories and Holography: It has been conjectured that Little String Theories in six dimensions are
holographic to critical string theory in a linear dilaton background. We test
this conjecture for theories arising on the worldvolume of heterotic
fivebranes. We compute the spectrum of chiral primaries in these theories and
compare with results following from Type I-heterotic duality and the AdS/CFT
correspondence. We also construct holographic duals for heterotic fivebranes
near orbifold singularities. Finally we find several new Little String Theories
which have Spin(32)/Z_2 or E_8 \times E_8 global symmetry but do not have a
simple interpretation either in heterotic or M-theory. |
Physical Properties of Quantum Field Theory Measures: Well known methods of measure theory on infinite dimensional spaces are used
to study physical properties of measures relevant to quantum field theory. The
difference of typical configurations of free massive scalar field theories with
different masses is studied. We apply the same methods to study the
Ashtekar-Lewandowski (AL) measure on spaces of connections. We prove that the
diffeomorphism group acts ergodically, with respect to the AL measure, on the
Ashtekar-Isham space of quantum connections modulo gauge transformations. We
also prove that a typical, with respect to the AL measure, quantum connection
restricted to a (piecewise analytic) curve leads to a parallel transport
discontinuous at every point of the curve. | Schwinger, ltd: Loop-tree duality in the parametric representation: We derive a variant of the loop-tree duality for Feynman integrals in the
Schwinger parametric representation. This is achieved by decomposing the
integration domain into a disjoint union of cells, one for each spanning tree
of the graph under consideration. Each of these cells is the total space of a
fiber bundle with contractible fibers over a cube. Loop-tree duality emerges
then as the result of first decomposing the integration domain, then
integrating along the fibers of each fiber bundle. As a byproduct we obtain a
new proof that the moduli space of graphs is homotopy equivalent to its spine.
In addition, we outline a potential application to Kontsevich's graph
(co-)homology. |
Solid quantization for non-point particles: In quantum field theory, elemental particles are assumed to be point
particles. As a result, the loop integrals are divergent in many cases.
Regularization and renormalization are necessary in order to get the physical
finite results from the infinite, divergent loop integrations. We propose new
quantization conditions for non-point particles. With this solid quantization,
divergence could be treated systematically. This method is useful for effective
field theory which is on hadron degrees of freedom. The elemental particles
could also be non-point ones. They can be studied in this approach as well. | Equation of motion of canonical tensor model and Hamilton-Jacobi
equation of general relativity: The canonical tensor model (CTM) is a rank-three tensor model formulated as a
totally constrained system in the canonical formalism. The constraint algebra
of CTM has a similar structure as that of the ADM formalism of general
relativity, and is studied as a discretized model for quantum gravity. In this
paper, we analyze the classical equation of motion (EOM) of CTM in a formal
continuum limit through a derivative expansion of the tensor up to the forth
order, and show that it is the same as the EOM of a coupled system of gravity
and a scalar field derived from the Hamilton-Jacobi equation with an
appropriate choice of an action. The action contains a scalar field potential
of an exponential form, and the system classically respects a dilatational
symmetry. We find that the system has a critical dimension, given by six, over
which it becomes unstable due to the wrong sign of the scalar kinetic term. In
six dimensions, de Sitter spacetime becomes a solution to the EOM, signaling
the emergence of a conformal symmetry, while the time evolution of the scale
factor is power-law in dimensions below six. |
Collective fermionic excitations in systems with a large chemical
potential: We study fermionic excitations in a cold ultrarelativistic plasma. We
construct explicitly the quantum states associated with the two branches which
develop in the excitation spectrum as the chemical potential is raised. The
collective nature of the long wavelength excitations is clearly exhibited.
Email contact: [email protected] | Mixmaster Horava-Witten Cosmology: We discuss various superstring effective actions and, in particular, their
common sector which leads to the so-called pre-big-bang cosmology (cosmology in
a weak coupling limit of heterotic superstring). Then, we review the main ideas
of the Horava-Witten theory which is a strong coupling limit of heterotic
superstring theory. Using the conformal relationship between these two theories
we present Kasner asymptotic solutions of Bianchi type IX geometries within
these theories and make predictions about possible emergence of chaos. Finally,
we present a possible method of generating Horava-Witten cosmological solutions
out of the well-known general relativistic pre-big-bang solutions. |
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